50 years of combinatorics, graph theory, and computing:
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| Other Authors: | |
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| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, FL
CRC Press, Taylor & Francis Group
[2020]
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| Series: | Discrete mathematics and its applications
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xxvi, 415 Seiten Illustrationen |
| ISBN: | 9780367235031 036723503X |
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| 245 | 1 | 0 | |a 50 years of combinatorics, graph theory, and computing |c edited by Fan Chung [and five others] |
| 246 | 1 | 3 | |a Fifty years of combinatorics, graph theory, and computing |
| 264 | 1 | |a Boca Raton, FL |b CRC Press, Taylor & Francis Group |c [2020] | |
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Record in the Search Index
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| adam_text | Contents Preface xv Editors xxiii Contributors xxv 1 Personal Reflections of the SEICCGTC: Origins and Beyond 1 K. B. Reid 1.1 Introduction.....................................................................................................1 1.2 Description of This Chapter ............................................................... 2 1.3 Impressions of the Combinatorial Research Atmosphere in the Late 1960’s............................................................ 3 1.4 Brief Biographies of Early Conference Organizers ......................... 6 1.5 Conference Facts.................................................................................. 9 1.6 Some Non-Conference Activitiesat the Conferences ....................... 11 1.7 Conference “Firsts” ............................................................................ 13 1.8 Some Mathematics from the Fifth Conference (1974)..................................................................................................... 14 1 Combinatorics 19 2 Some of My Favorite Problems (I) Ron Graham 2.1 Introduction............................................................................................ 2.2 Prologue ............................................................................................... 2.3 Universal Cycles.................................................................................. 2.4 Combs .................................................................................................. 2.5 The Middle Binomial Coefficient (2՞)............................................. 2.6 The
Steiner Ratio Problem................................................................... 2.7 A Curious ‘Inversion’ in Complexity Theory ................................... 2.8 A Final Problem .................................................................................. 21 3 Variations on the Sequenceable Theme Brian Alspach 3.1 Introduction............................................................................................ 3.2 Strongly Sequenceable Groups............................................................ 3.3 Orthogonal Decompositions............................................................... 21 21 22 24 26 28 30 32 37 37 40 41 vii
Contents viii 3.4 3.5 3.6 3.7 3.8 3.9 4 5 6 Abelian Groups...................................................................................... A Poset Formulation............................................................................ The Poset Approach ............................................................................ Partial Steiner Triple Systems .......................................................... Other Decompositions ......................................................................... Sequencing Edges ............................................................................... 42 44 46 47 50 50 A Survey of Stack Sortable Permutations Miklós Bòna 4.1 Introduction............................................................................................ 4.2 Three Equivalent Definitions................................................................ 4.2.1 The Original Definition............................................................. 4.2.2 The Original DefinitionRevisited........................................... 4.2.3 The Definition Using Trees...................................................... 4.3 Enumeration Formulas......................................................................... 4.3.1 Exact Formulas......................................................................... 4.3.2 A Surprising Connection with the Pattern 1324 ................... 4.3.3 Bounds...................................................................................... 4.3.3.1 Stack Words............................................................
4.3.3.2 Computing the Upper Bound for Wį(n)................. 4.4 The Generating Function of theNumbers Wt (n)................................. 4.5 Descents ............................................................................................... 4.6 Further Directions ............................................................................... 55 Dimension for Posets and Chromatic Number for Graphs William T Trotter 5.1 Introduction............................................................................................ 5.1.1 Basic Concepts and Results for Dimension......................... 5.2 Stability Analysis................................................................................... 5.2.1 Stability Analysis for Dimension............................................. 5.2.2 Open Problems for Stability Analysis................................... 5.2.3 Open Problems on Size............................................................ 5.3 Maximum Degree ............................................................................... 5.4 Blocks in Posets and Graphs................................................................ 5.4.1 Open Problems Involving Cover Graphs . ............................. 73 Erdos Magic Joel Spencer 6.1 Introduction............................................................................................ 6.2 Independent Sets................................................................................... 6.3 Avoiding Monochromatic Sets............................................................ 6.4 Six Suffice
............................................................................................ 6.5 QuasiRandomness ............................................................................... 6.6 Graphons............................................................................................... 97 55 56 56 56 57 58 58 60 61 61 63 65 67 70 73 74 76 79 81 82 83 88 90 97 98 99 102 104 105
Contents II Graph Theory 7 8 ix 109 Developments on Saturated Graphs Ronald J. Gould 7.1 Introduction............................................................................................ 7.2 Saturation Numbers ............................................................................ 7.2.1 Trees and Forests...................................................................... 7.2.2 Cycles......................................................................................... 7.2.3 Partite Graphs............................................................................ 7.3 Limits On The Saturation Function ................................................... 7.4 Hypergraphs ......................................................................................... 7.5 Saturation Spectrum ............................................................................ 7.6 Variations............................................................................................... 7.6.1 Weak Saturation...................................................................... 7.6.2 Edge-Colored Saturation......................................................... 7.6.3 Other Variations and Results................................................... 111 Magic Labeling Basics W. D. Wallis 8.1 Magic Labeling...................................................................................... 8.1.1 Labelings.................................................................................. 8.1.2 The Classical Magic Arrays................................................... 8.1.3 Magic
Labeling......................................................................... 8.2 Edge-Magic Total Labelings............................................................... 8.2.1 Basic Ideas............................................................................... 8.2.1.1 Definitions................................................................ 8.2.1.2 Some Elementary Counting................................... 8.2.1.3 Duality....................................................................... 8.2.2 Cliques and Complete Graphs................................................ 8.2.2.1 Sidon Sequences....................................................... 8.2.2.2 Complete Subgraphs................................................ 8.2.3 Cycles......................................................................................... 8.2.3.1 Generalizations of Cycles....................................... 8.2.4 Complete Bipartite Graphs...................................................... 8.2.5 Trees......................................................................................... 8.3 Vertex-Magic Total Labelings ............................................................ 8.3.1 Basic Ideas............................................................................... 8.3.1.1 Definitions................................................................ 8.3.1.2 Basic Counting ....................................................... 8.3.2 Regular Graphs......................................................................... 8.3.3 Some Standard
Graphs............................................................ 8.3.3.1 Cycles and Paths....................................................... 8.3.3.2 Complete Graphs and Complete Bipartite Graphs...................................................................... 8.3.3.3 Construction of VMTLs of Km,n.............................. 135 Ill 113 114 117 117 118 119 120 124 124 127 128 136 136 136 137 138 138 138 138 140 140 140 142 143 143 143 144 145 145 145 145 147 147 147 147 149
x Contents 8.3.3.4 Joins......................................................................... Graphs with Vertices of Degree One...................................... 149 149 Block Colorings of Graph Decompositions E. B. Matson and C. A. Rodger 9.1 Introduction............................................................................................ 9.2 Graph Decompositions......................................................................... 9.3 Amalgamations and Recent Results ................................................... 9.4 Open Problems...................................................................................... 155 10 Reconfiguration of Colourings and Dominating Sets in Graphs C. M. Mynhardt and S. Nasserasr 10.1 Introduction............................................................................................ 10.2 Complexity............................................................................................ 10.3 Reconfiguration of Colourings............................................................. 10.3.1 The ¿-Colouring Graph............................................................ 10.3.2 Reconfiguration of Homomorphisms...................................... 10.3.3 The Ä-Edge-Colouring Graph ................................................ 10.4 Reconfiguration of Dominating Sets................................................... 10.4.1 The ^-Dominating Graph......................................................... 10.4.2 The ^-Total-Dominating Graph................................................ 10.4.3 Jump
y-Graphs......................................................................... 10.4.4 Slide y-Graphs......................................................................... 10.4.5 Irredundance............................................................................ 171 8.3.4 9 155 159 161 166 171 173 174 174 179 180 181 181 184 185 186 186 11 Edge Intersection Graphs of Paths on a Grid 193 Martin Charles Golumbic and Gila Morgenstern 11.1 Introduction............................................................................................ 194 11.2 The Bend Number of Known Classes of Graphs................................ 194 11.3 B i-Subclass Characterizations............................................................ 196 11.4 The Strong Helly Number of 5i֊EPG Representations...................................................................................... 201 11.5 Algorithmic Aspects of EPG Graphs......................................................202 11.6 Boundary Generated B -EPG Graphs ....................................................204 11.7 Concluding Remarks and Further Reading.............................................206 III Combinatorial Matrix Theory 211 12 A Jaunt in Spectral Graph Theory 213 Steve Butler 12.1 Introduction................................................................................................ 214 12.2 A Menagerie of Matrices...................................................................... 214 12.2.1 The Adjacency Matrix............................................................ 214 12.2.2 The Laplacian Matrix
and Signless Laplacian Matrix .... 216
Contents xi 12.2.3 The Probability Transition Matrix and the Normalized Laplacian.................................................................................. 218 12.2.4 The Distance Matrix................................................................... 221 12.2.5 The Seidel Matrix .......................................................................222 12.2.6 The Quantum Walk Matrix..........................................................223 12.3 Strengths and Weaknesses of Different Matrices .............................223 12.3.1 Combining Spectra................................................................... 224 12.3.2 Graph Operations..........................................................................224 12.3.3 A Line Graph Excursion............................................................. 226 12.3.4 Graphs Determined by Their Spectrum ................................ 227 12.3.5 Interlacing ................................................................................... 228 12.3.6 Graphs that Have a Common Spectrum....................................228 12.4 Connectivity .............................................................................................230 12.4.1 Bottlenecks and Cheeger Constants.......................................... 230 12.4.2 Discrepancy and the Value of Normalizing ............................. 231 12.4.3 Ramanujan Graphs.......................................................................233 12.4.4 Quasirandom Graphs................................................................... 233 12.5 Starting Your
Odyssey in Spectral Graph Theory .................................234 13 The Inverse Eigenvalue Problem of a Graph 239 Leslie Hogben, Jephian C.-H. Lin, and Bryan L. Shader 13.1 Introduction................................................................................................ 239 13.2 Ancillary Problems................................................................................... 242 13.2.1 Maximum Nullity and Minimum Rank ....................................243 13.2.2 Variants of Maximum Nullity and Minimum Rank.................244 13.2.3 The Minimum Number of Distinct Eigenvalues....................... 245 13.3 Strong Properties and Minor Monotonicity ...................................... 246 13.3.1 Applications of the Strong Properties....................................... 247 13.3.2 Tangent Spaces and the Implicit Function Theorem.............250 13.4 Zero Forcing, Propagation Time, and Throttling................................ 252 13.4.1 Zero Forcing and Its Variants.......................................................252 13.4.2 Propagation Time...................................................................... 255 13.4.3 Throttling...................................................................................... 256 13.5 Concluding Remarks and Open Problems............................................. 257 14 Rank Functions 263 LeRoy B. Beasley 14.1 Introduction................................................................................................263 14.2
Preliminaries.............................................................................................264 14.3 Matrix Ranks......................................................................................... 266 14.4 Rank Functions in Graph Theory ...................................................... 269 14.4.1 Minimum Rank.............................................................................269 14.4.2 Rank Functions on Graphs Defined by Coverings....................270 14.4.3 Rank Functions on Graphs Not Defined by Coverings .... 272 14.5 Equivalent Rank Functions.......................................................................272
xii Contents 15 Permutation Matrices and Beyond: An Essay 277 Richard A. Brualdi 15.1 Permutation Matrices............................................................................ 277 15.2 Beyond Permutation Matrices ................................................................ 278 15.3 Some Favorite Matrices in These Classes ............................................. 286 IV Designs, Geometry, Packing and Covering 291 16 Some New Families of 2-Resolutions 293 Michael Hurley, Oscar Lopez, and Spyros S. Magliveras 16.1 Introduction................................................................................................ 293 16.2 Preliminaries.............................................................................................294 16.3 Incidence Matrices................................................................................... 295 16.4 The Half-Affine Group......................................................................... 297 16.5 A New Family of 2-Resolutions ............................................................. 297 16.6 Conclusion................................................................................................299 17 Graphical Designs 301 Donald L. Kreher 17.1 Introduction............................................................................................ 301 17.2 Graphical Designs ............................................................................... 302 17.3 Orbits of Sn Acting on E(Kn) ................................................................ 302 17.4 Steiner Graphical Designs
................................................................... 304 17.5 Steiner Bigraphical Designs ................................................................ 310 17.5.1 Remarks on the 5-(16, {6,8}, 1) Design................................ 311 17.6 Steiner Graphical Designs of Type nr ................................................ 311 17.7 Higher Index ......................................................................................... 312 17.8 Historical Remarks............................................................................... 314 18 There Must be Fifty Ways to Miss a Cover 319 Charles J. Colboum and Violet R. Syrotiuk 18.1 Introduction............................................................................................ 319 18.2 Combinatorics of Interaction Testing ................................................ 320 18.2.1 Covering Arrays...................................................................... 321 18.2.2 Locating and Detecting Arrays................................................ 321 18.2.3 Prior Work................................................................................... 322 18.3 A Construction from One-factorizations.................................................323 18.4 Concluding Remarks................................................................................ 330 19 Combinatorial Designs and Cryptography, Revisited 335 Douglas R. Stinson 19.1 Introduction............................................................................................ 336 19.2 The One-time Pad and Shannon’s
Theory......................................... 337
Contents 19.3 Threshold Schemes and Ramp Schemes............................................ 19.3.1 Ramp Schemes......................................................................... 19.4 All-or-Nothing Transforms................................................................... 19.4.1 Binary AONT with f = 2......................................................... 19.4.2 General AONT with t = 2...................................................... 19.5 Algebraic Manipulation Detection Codes ......................................... 19.5.1 Weak and Strong AMD Codes................................................ 19.5.2 An Application of AMD Codes to Threshold Schemes . . . 19.5.3 Combinatorial Analysis of AMD Codes................................ 19.5.4 Nonuniform AMD Codes ...................................................... 19.6 Conclusion and Open Problems ......................................................... xiii 339 341 343 344 346 347 347 348 349 352 354 20 A Survey of Scalar Multiplication Algorithms 359 Ko ray Karabina 20.1 Introduction............................................................................................ 359 20.1.1 Cryptographic Applications................................................... 360 20.1.2 Multidimensional Scalar Multiplication and Endomorphisms ...................................................................... 361 20.1.3 Signed Digit Recodings and Differential Additions.............362 20.1.4 Side Channel Attacks and Regular Recodings.......................... 363 20.1.5 Organization of the Chapter . .
:......................................... 363 20.2 Variable Scalar and Variable Base...................................................... 365 20.2.1 Width-w Window Methods..........................................................365 20.2.2 Signed Digit Recoding Methods............................................ 369 20.2.3 Regular Recoding Methods...................................................... 372 20.3 Variable Scalar and Fixed Base ......................................................... 375 20.3.1 Split and Comb Methods......................................................... 376 20.3.2 A Euclidean Type Algorithm.......................................................379 20.3.3 Regular Recoding Methods...................................................... 380 21 Arcs, Caps, Generalisations: Results and Problems 387 Joseph A. Thas 21.1 Introduction ......................................................................................... 387 21.2 k-Arcs ofPG(2,#)................................................................................... 388 21.3 Complete Arcs...................................................................................... 389 21.4 k-Caps and О voids............................................................................... 391 21.5 Ovoids and Inversive Planes............................................................... 393 21.6 k-Caps and Cap-Codes.............................................................................394 21.7 k-Caps in PG(n,i7),n 3 ................................................................... 395 21.8
Generalised k-Arcs and Generalised k-Caps ................................... 397 21.9 Generalised Ovals and Ovoids............................................................ 398 21.10 Regular Pseudo-Ovals and Pseudo-0voids .......................................... 400 21.11 Translation Duals ................................................................................... 400
xiv Contents 21.12 Characterisations of Pseudo-Ovals and Pseudo-Ovoids....................... 401 21.13 Problems................................................................................................... 403 21.13.1 Problems on Arcs.......................................................................403 21.13.2 Problems on Caps.......................................................................403 21.13.3 Problems on Generalised k-Arcs and Generalised -Caps..........................................................................................403 Index 409
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| spelling | 50 years of combinatorics, graph theory, and computing edited by Fan Chung [and five others] Fifty years of combinatorics, graph theory, and computing Boca Raton, FL CRC Press, Taylor & Francis Group [2020] xxvi, 415 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Discrete mathematics and its applications Kombinatorik (DE-588)4031824-2 gnd rswk-swf Graphentheorie (DE-588)4113782-6 gnd rswk-swf Combinatorial analysis (DE-588)4143413-4 Aufsatzsammlung gnd-content Kombinatorik (DE-588)4031824-2 s Graphentheorie (DE-588)4113782-6 s DE-604 Chung Graham, Fan 1949- (DE-588)112177042 edt Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031829806&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| title | 50 years of combinatorics, graph theory, and computing |
| title_alt | Fifty years of combinatorics, graph theory, and computing |
| title_auth | 50 years of combinatorics, graph theory, and computing |
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| title_full | 50 years of combinatorics, graph theory, and computing edited by Fan Chung [and five others] |
| title_fullStr | 50 years of combinatorics, graph theory, and computing edited by Fan Chung [and five others] |
| title_full_unstemmed | 50 years of combinatorics, graph theory, and computing edited by Fan Chung [and five others] |
| title_short | 50 years of combinatorics, graph theory, and computing |
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