Fractional graph theory: a rational approach to the theory of graphs
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Mineola, NY
Dover Publ.
2011
|
| Edition: | unabridged republ. of the work originally publ. in 1997 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 191 - 203 |
| Physical Description: | XVII, 211 S. graph. Darst. |
| ISBN: | 9780486485935 0486485935 |
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Record in the Search Index
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|---|---|
| adam_text | Contents Foreword xi Preface xiii 1 General Theory: Hypergraphs i Hypergraph covering and packing Fractional covering and packing Some consequences A game-theoretic approach Duality and duality Asymptotic covering and packing Exercises Notes 2 3 5 7 8 10 16 17 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 2 Fractional Matching 2.1 2.2 2.3 2.4 2.5 2.6 19 Introduction Results on maximum fractional matchings Fractionally Hamiltonian graphs Computational complexity Exercises Notes 3 Fractional Coloring 3.1 3.2 3.3 3.4 3.5 19 24 29 36 37 39 41 Definitions Homomorphisms and the Kneser graphs The duality gap Graph products The asymptotic chromatic and clique numbers vii 41 43 48 52 56
viii Contents 3.6 3.7 3.8 3.9 3.10 3.11 4 5 . 59 66 69 71 72 75 Fractional Edge Coloring 77 4.1 Introduction 4.2 An exact formula 4.3 The matching polytope 4.4 Proof and consequences 4.5 Computational complexity 4.6 Fractional total chromatic number 4.7 Exercises 4.8 Notes 77 79 80 83 86 87 95 97 Fractional Arboricity and Matroid Methods 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 6 The fractional chromatic number of the plane The Erdős-Faber-Lovász conjecture List coloring Computational complexity Exercises Notes Arboricity and maximum average degree Matroid theoretic tools Matroid partitioning Arboricity again Maximum average degree again Duality, duality, duality, and edge toughness Exercises Notes Fractional Isomorphism 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 Relaxing isomorphism Linear algebra tools Equitable partitions Iterated degree sequences The main theorem Other relaxations of isomorphism Exercises Notes ’ 99 99 101 106 112 115 117 124 126 127 127 132 137 139 140 144 148 150
Contents;ix 7 Fractional Odds and Ends 7.1 Fractional topological graph theory 7.2 Fractional cycle double covers 7.3 Fractional Ramsey theory 7.4 Fractional domination 7.5 Fractional intersection number 7.6 Fractional dimension of a poset 7.7 Sperner’s theorem: a fractional perspective 7.8 Exercises 7.9 Notes Appendix: Background A. 1 A.2 A.3 A.4 A.5 A.6 Basic graph theory and notation Hypergraphs, multigraphs, multisets, fuzzy sets Linear programming The subadditivity lemma Exercises Notes i52 շ 52 ] 55 157 ¡gø 167 172 175 լ 7g 17g i80 181 184 185 188 100 j gø Bibliography 191 Author Index 203 Subject Index 9Ո7
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| any_adam_object | 1 |
| author | Scheinerman, Edward Ullman, Daniel H. |
| author_GND | (DE-588)113762938X (DE-588)143306944 |
| author_facet | Scheinerman, Edward Ullman, Daniel H. |
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| author_sort | Scheinerman, Edward |
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| bvnumber | BV041241949 |
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| ctrlnum | (OCoLC)721885660 (DE-599)OBVAC08773184 |
| dewey-full | 511.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.5 |
| dewey-search | 511.5 |
| dewey-sort | 3511.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | unabridged republ. of the work originally publ. in 1997 |
| format | Book |
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| id | DE-604.BV041241949 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:42:58Z |
| institution | BVB |
| isbn | 9780486485935 0486485935 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026216137 |
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| physical | XVII, 211 S. graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
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| publisher | Dover Publ. |
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| spelling | Scheinerman, Edward Verfasser (DE-588)113762938X aut Fractional graph theory a rational approach to the theory of graphs Edward R. Scheinerman ; Daniel H. Ullman unabridged republ. of the work originally publ. in 1997 Mineola, NY Dover Publ. 2011 XVII, 211 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 191 - 203 Graphentheorie (DE-588)4113782-6 gnd rswk-swf Graphentheorie (DE-588)4113782-6 s DE-604 Ullman, Daniel H. Verfasser (DE-588)143306944 aut 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=026216137&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Scheinerman, Edward Ullman, Daniel H. Fractional graph theory a rational approach to the theory of graphs Graphentheorie (DE-588)4113782-6 gnd |
| subject_GND | (DE-588)4113782-6 |
| title | Fractional graph theory a rational approach to the theory of graphs |
| title_auth | Fractional graph theory a rational approach to the theory of graphs |
| title_exact_search | Fractional graph theory a rational approach to the theory of graphs |
| title_full | Fractional graph theory a rational approach to the theory of graphs Edward R. Scheinerman ; Daniel H. Ullman |
| title_fullStr | Fractional graph theory a rational approach to the theory of graphs Edward R. Scheinerman ; Daniel H. Ullman |
| title_full_unstemmed | Fractional graph theory a rational approach to the theory of graphs Edward R. Scheinerman ; Daniel H. Ullman |
| title_short | Fractional graph theory |
| title_sort | fractional graph theory a rational approach to the theory of graphs |
| title_sub | a rational approach to the theory of graphs |
| topic | Graphentheorie (DE-588)4113782-6 gnd |
| topic_facet | Graphentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026216137&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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