Digraphs: theory, algorithms and applications
Gespeichert in:
| Hauptverfasser: | , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London [u.a.]
Springer
2009
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Springer monographs in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXII, 795 Seiten Diagramme |
| ISBN: | 9780857290410 9781848009974 |
Internformat
MARC
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| 100 | 1 | |a Bang-Jensen, Jørgen |d 1960- |e Verfasser |0 (DE-588)142714992 |4 aut | |
| 245 | 1 | 0 | |a Digraphs |b theory, algorithms and applications |c Jørgen Bang-Jensen ; Gregory Gutin |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a London [u.a.] |b Springer |c 2009 | |
| 300 | |a XXII, 795 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer monographs in mathematics | |
| 650 | 4 | |a Directed graphs | |
| 650 | 0 | 7 | |a Graphentheorie |0 (DE-588)4113782-6 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Gutin, Gregory Z. |d 1957- |e Verfasser |0 (DE-588)142715557 |4 aut | |
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Datensatz im Suchindex
| _version_ | 1818888938912219136 |
|---|---|
| adam_text |
Contents
1. Basic
Terminology,
Notation
and Results
. 1
1.1
Sets, Matrices and Vectors
. 1
1.2
Digraphs, Subdigraphs, Neighbours, Degrees
. 2
1.3
Isomorphism and Basic Operations on Digraphs
. 6
1.4
Walks, Trails, Paths, Cycles and Path-Cycle Subdigraphs
_ 11
1.5
Strong and Unilateral Connectivity
. 15
1.6
Undirected Graphs, Biorientations and Orientations
. 18
1.7
Trees and
Euler
Trails in Digraphs
. 21
1.8
Mixed Graphs, Orientations of Digraphs, and Hypergraphs
. . 24
1.9
Depth-First Search
. 26
1.10
Exercises
. 29
2.
Classes of Digraphs
. 31
2.1
Acyclic Digraphs
. 32
2.2
Multipartite Digraphs and Extended Digraphs
. 34
2.3
Transitive Digraphs, Transitive Closures and Reductions
. 36
2.4
Line Digraphs
. 39
2.5
The
de Bruijn
and Kautz Digraphs
. 44
2.6
Series-Parallel Digraphs
. 47
2.7
Quasi-Transitive Digraphs
. 52
2.8
Path-Mergeable Digraphs
. 55
2.9
Locally In/Out-Semicomplete Digraphs
. 57
2.10
Locally Semicomplete Digraphs
. 59
2.10.1
Round Digraphs
. 60
2.10.2
Non-Strong Locally Semicomplete Digraphs
. 61
2.10.3
Strong Round Decomposable Locally Semicomplete
Digraphs
. 63
2.10.4
Classification of Locally Semicomplete Digraphs
. 66
2.11
Totally (^-Decomposable Digraphs
. 69
2.12
Planar Digraphs
. 71
2.13
Digraphs of Bounded Width
. 73
2.13.1
Digraphs of Bounded Tree-Width
. 74
2.13.2
Digraphs of Bounded Directed Widths
. 78
2.14
Other Families of Digraphs
. 80
xiv Contents
2.14.1
Circulant
Digraphs
. 80
2.14.2
Arc-Locally
Semicomplete
Digraphs
. 81
2.14.3
Intersection Digraphs
. 82
2.15
Exercises
. 84
3.
Distances
. 87
3.1
Terminology and Notation on Distances
. 87
3.2
Structure of Shortest Paths
. 89
3.3
Algorithms for Finding Distances in Digraphs
. 91
3.3.1
Breadth-First Search (BFS)
. 92
3.3.2
Acyclic Digraphs
. 93
3.3.3
Dijkstra's
Algorithm
. 94
3.3.4
The Bellman-Ford-Moore Algorithm
. 97
3.3.5
The Floyd-
Warshall
Algorithm
. 99
3.4
Inequalities on Diameter
. 100
3.5
Minimum Diameter of Orientations of Multigraphs
. 103
3.6
Minimum Diameter Orientations of Some Graphs and DigraphslO8
3.6.1
Generalizations of Tournaments
.108
3.6.2
Extended Digraphs
.
Ill
3.6.3
Cartesian Products of Graphs
.113
3.6.4
Chordal Graphs
.114
3.7
Kings in Digraphs
.115
3.7.1 2-
Kings in Tournaments
.115
3.7.2
Kings in
Semicomplete
Multipartite Digraphs
.116
3.7.3
Kings in Generalizations of Tournaments
.118
3.8
(k. ^-Kernels
.119
3.8.1
Kernels
.119
3.8.2
Quasi-Kernels
.122
3.9
Exercises
.123
4.
Flows in Networks
.127
4.1
Definitions and Basic Properties
.127
4.1.1
Flows and Their Balance Vectors
.128
4.1.2
The Residual Network
.130
4.2
Reductions Among Different Flow Models
.131
4.2.1
Eliminating Lower Bounds
.131
4.2.2
Flows with One Source and One Sink
.132
4.2.3
Circulations
.133
4.2.4
Networks with Bounds and Costs on the Vertices
.134
4.3
Flow Decompositions
.136
4.4
Working with the Residual Network
.137
4.5
The Maximum Flow Problem
.140
4.5.1
The Ford-Fulkerson Algorithm
.142
4.5.2
Maximum Flows and Linear Programming
.145
4.6
Polynomial Algorithms for Finding a Maximum
(s.ť)-Flow
.146
Contents xv
4.6.1
Augmenting Along Shortest Augmenting Paths
.147
4.6.2
Maximal Flows in Layered Networks
.148
4.6.3
The Push-Relabel Algorithm
.149
4.7
Unit Capacity Networks and Simple Networks
.153
4.7.1
Unit Capacity Networks
.153
4.7.2
Simple Networks
.155
4.8
Circulations and Feasible Flows
.156
4.9
Minimum Value Feasible (s, i)-Flows
.158
4.10
Minimum Cost Flows
.160
4.10.1
Characterizing Minimum Cost Flows
. 162
4.10.2
Building up an Optimal Solution
. 166
4.10.3
The Assignment and the Transportation Problem
. 169
4.11
Applications of Flows
. 170
4.11.1
Maximum Matchings in Bipartite Graphs
.170
4.11.2
The Directed Chinese Postman Problem
.174
4.11.3
Finding Subdigraphs with Prescribed Degrees
.176
4.11.4
Path-Cycle Factors in Directed Multigraphs
.177
4.12
Exercises
.179
5.
Connectivity of Digraphs
.191
5.1
Additional Notation and Preliminaries
.192
5.1.1
The Network Representation of a Directed Multigraph
194
5.2
Finding the Strong Components of a Digraph
.195
5.3
Ear Decompositions
.198
5.4
Menger's Theorem
.201
5.5
Determining Arc- and Vertex-Strong Connectivity
.204
5.6
Minimally fc-(Arc)-Strong Directed Multigraphs
.207
5.6.1
Minimally k-Arc-Strong Directed Multigraphs
.207
5.6.2
Minimally fc-Strong Digraphs
.213
5.7
Critically /c-Strong Digraphs
.218
5.8
Connectivity Properties of Special Classes of Digraphs
.220
5.9
Disjoint
Х
-Paths in Digraphs
.223
5.10
Exercises
.223
6.
Hamiltonian, Longest and Vertex-Cheapest Paths and Cy¬
cles
.227
6.1
Complexity
.228
6.2
Hamilton Paths and Cycles in Path-Mergeable Digraphs
.230
6.3
Hamilton Paths and Cycles in Locally In-Semicomplete Di¬
graphs
.231
6.4
Hamilton Cycles and Paths in Degree-Constrained Digraphs
. 233
6.4.1
Sufficient Conditions
.233
6.4.2
The Multi-Insertion Technique
.239
6.4.3
Proofs of Theorems
6.4.1
and
6.4.5 .240
xvi Contents
6.5
Longest Paths and Cycles in Degree-Constrained Oriented
Graphs
.243
6.6
Longest Paths and Cycles in
Semicomplete
Multipartite Di¬
graphs
.244
6.6.1
Basic Results
. 245
6.6.2
The Good Cycle Factor Theorem
. 247
6.6.3
Consequences of Lemma
6.6.12. 250
6.6.4
Yeo's Irreducible Cycle Subdigraph Theorem and Its
Applications
. 253
6.7
Hamilton Paths and Cycles in Quasi-Transitive Digraphs
. 256
6.8
Vertex-Cheapest Paths and Cycles
. 260
6.8.1
Vertex-Cheapest Paths and Cycles in Quasi-Transitive
Digraphs
.260
6.8.2
Minimum Cost fc-Path-Cycle Subdigraphs
.261
6.8.3
Cheapest
г
-Path
Subdigraphs in Quasi-Transitive Di¬
graphs
.263
6.8.4
Finding a Cheapest Cycle in a Quasi-Transitive Digraph265
6.9
Hamilton Paths and Cycles in Various Classes of Digraphs
. . . 265
6.10
Exercises
.271
7.
Restricted Hamiltonian Paths and Cycles
.275
7.1
Hamiltonian Paths with a Prescribed End-Vertex
.275
7.2
Weakly Hamiltonian-Connected Digraphs
.277
7.2.1
Results for Extended Tournaments
.277
7.2.2
Results for Locally
Semicomplete
Digraphs
.283
7.3
Hamiltonian-Connected Digraphs
.286
7.4
Hamiltonian Cycles Containing or Avoiding Prescribed Arcs
. 289
7.4.1
Hamiltonian Cycles Containing Prescribed Arcs
. 290
7.4.2
Avoiding Prescribed Arcs with a Hamiltonian Cycle
. . 292
7.4.3
Hamiltonian Cycles Avoiding Arcs in 2-Cycles
. 295
7.5
Arc-Traceable Digraphs
. 296
7.6
Oriented Hamiltonian Paths and Cycles
. 297
7.7
Exercises
. 303
8.
Paths and Cycles of Prescribed Lengths
.307
8.1
Pancyclicity of Digraphs
.307
8.1.1
(Vertex-)Pancyclicity in Degree-Constrained Digraphs.
308
8.1.2
Pancyclicity in Extended
Semicomplete
and Quasi-
Transitive Digraphs
.309
8.1.3
Pancyclic and Vertex-Pancyclic Locally
Semicomplete
Digraphs
.312
8.1.4
Further Pancyclicity Results
.315
8.1.5
Cycle Extendability in Digraphs
.317
8.1.6
Arc-Pancyclicity
.318
8.2
Colour Coding: Efficient Algorithms for Paths and Cvcles
. . . 320
Contents xvii
8.3
Cycles
of Length
к
Modulo
ρ.
324
8.3.1
Complexity of the Existence of Cycles of Length
к
Modulo
ρ
Problems
.324
8.3.2
Sufficient Conditions for the Existence of Cycles of
Length
к
Modulo
ρ
.326
8.4
Girth
.329
8.5
Short Cycles in Semicomplete Multipartite Digraphs
.332
8.6
Exercises
.336
9.
Branchings
.339
9.1
Tutte's Matrix Tree Theorem
.339
9.2
Optimum Branchings
.342
9.2.1
Matroid Intersection Formulation
.343
9.2.2
A Simple Algorithm for Finding a Minimum Cost Out-
Branching
.344
9.3
Arc-Disjoint Branchings
.345
9.4
Implications of Edmonds' Branching Theorem
.348
9.5
Out-Branchings with Degree Bounds
.351
9.6
Arc-Disjoint In- and Out-Branchings
.354
9.7
Out-Branchings with Extremal Number of Leaves
.358
9.7.1
Minimum Leaf Out-Branchings
.359
9.7.2
Maximum Leaf Out-Branchings
.361
9.8
The Source Location Problem
.363
9.9
Miscellaneous Topics
.365
9.9.1
Edge-Disjoint Mixed Branchings
.365
9.9.2
The Minimum Covering Out-Tree Problem
.366
9.9.3
Minimum Cost Arc-Disjoint Branchings with Band¬
width Constraints
.367
9.9.4
Out-Forests
.368
9.9.5
The Maximum Weight Out-Forest Problem
.368
9.9.6
Branchings and Edge-Disjoint Trees
.370
9.10
Exercises
.370
10.
Linkages in Digraphs
.373
10.1
Additional Definitions and Preliminaries
.373
10.2
The Complexity of the fc-Linkage Problem
.375
10.3
Sufficient Conditions for a Digraph to Be fc-Linked
.379
10.4
The fc-Linkage Problem for Acyclic Digraphs
.382
10.5
Linkages in (Generalizations of) Tournaments
.385
10.5.1
Sufficient Conditions in Terms of (Local-)Connectivity
385
10.5.2
The 2-Linkage Problem for Semicomplete Digraphs
. . . 389
10.5.3
The 2-Linkage Problem for Generalizations of Tourna¬
ments
.391
10.6
Linkages in Planar Digraphs
.394
10.7
Weak Linkages
.398
xviii Contents
10.7.1
Weak Linkages in Acyclic Directed Multigraphs
.400
10.7.2
Weak Linkages in Eulerian Directed Multigraphs
.401
10.7.3
Weak Linkages in Tournaments and Generalizations of
Tournaments
.407
10.8
Linkages in Digraphs with Large Minimum Out-Degree
.410
10.8.1
Subdivisions of Transitive Tournaments in Digraphs of
Large Out-Degree
.411
10.9
Miscellaneous Topics
.412
10.9.1
Universal Arcs in 2-Cyclic Digraphs
.412
10.9.2
Integer Multicommodity Flows
.413
10.10
Exercises
.414
11.
Orientations of Graphs and Digraphs
.417
11.1
Underlying Graphs of Various Classes of Digraphs
.417
11.1.1
Underlying Graphs of Transitive and Quasi-Transitive
Digraphs
.418
11.1.2
Underlying Graphs of Locally
Semicomplete
Digraphs
. 421
11.1.3
Local Tournament Orientations of Proper Circular Arc
Graphs
.423
11.1.4
Underlying Graphs of Locally
In-Semicomplete Digraphs
.426
11.2
Orientations with No Even Cycles
.428
11.3
Colourings and Orientations of Graphs
.431
11.4
Orientations and Nowhere-Zero Integer Flows
.435
11.5
Orientations Achieving High Arc-Strong Connectivity
.441
11.5.1
fc-Arc-Strong Orientations
.441
11.5.2
Well-Balanced and Best-Balanced Orientations
.443
11.5.3
Simultaneous Best-Balanced Orientations
.444
11.5.4
Best-Balanced Orientations of Eulerian Multigraphs
. 445
11.6
/с
-Strong Orientations
.446
11.7
Orientations Respecting Degree Constraints
.448
11.7.1
Orientations with Prescribed Degree Sequences
.448
11.7.2
Restrictions on Subsets of Vertices
.452
11.8
Submodular
Flows
.453
11.8.1
Submodular
Flow Models
.454
11.8.2
Existence of Feasible
Submodular
Flows
.455
11.8.3
Minimum Cost
Submodular
Flows
.458
11.8.4
Applications of
Submodular
Flows
.459
11.9
Orientations of Mixed Multigraphs
.461
11.10
/c-(Arc)-Strong Orientations of Digraphs
.466
11.11
Aliscellaneous Topics
.470
11.11.1
Another Measure of Well-Balancedness
.470
ll.ll^Orienting to Preserve Reachability
for Prescribed Pairs
.470
11.12
Exercises
.472
Contents xix
12.
Sparse
Subdigraphs
with Prescribed Connectivity
.479
12.1
Minimum Strong Spanning Subdigraphs
.480
12.1.1
Digraphs with High Minimum Degree
.482
12.2
Polynomially Solvable Cases of the MSSS Problem
.483
12.2.1
The MSSS Problem for Extended
Semicomplete
Digraphs
.484
12.2.2
The MSSS Problem for Quasi-Transitive Digraphs
_485
12.3
Approximation Algorithms for the MSSS Problem
.487
12.3.1
A Simple ^-Approximation Algorithm
.487
12.3.2
Better Approximation Algorithms
.488
12.4
Small Certificates for /c-(Arc)-Strong Connectivity
.489
12.4.1
Small Certificates for
/с
-Strong Connectivity
.490
12.4.2
Small Certificates for fc-Arc-Strong Connectivity
.491
12.4.3
Certificates for Directed Multigraphs
.494
12.5
Minimum Weight Strong Spanning Subdigraphs
.497
12.6
Directed
Steiner
Problems
.498
12.7
Miscellaneous Topics
.501
12.7.1
The Directed Spanning Cactus Problem
.501
12.7.2
An FTP Algorithm for the MSSS Problem
.501
12.7.3
Minimum Cost Strong Subdigraphs
.502
12.8
Exercises
.503
13.
Packings, Coverings and Decompositions
.505
13.1
Packing Directed Cuts: The
Lucchesi-
Younger Theorem
.505
13.2
Packing Dijoins:
Woodalľs
Conjecture
.511
13.3
Packing Cycles
.512
13.4
Arc-Disjoint Hamiltonian Paths and Cycles
.515
13.5
Path Factors
.519
13.6
Cycle Factors with the Minimum Number of Cycles
.521
13.7
Cycle Factors with a Fixed Number of Cycles
.525
13.8
Cycle Subdigraphs Covering Specified Vertices
.528
13.9
Proof of
Gallaľs
Conjecture
.529
13.10
Decomposing a Tournament into Strong
Spanning Subdigraphs
.536
13.11
The Directed Path-Partition Conjecture
.542
13.12
Miscellaneous Topics
.546
13.12.1
Maximum One-Way Cuts and Covering by One-Way
Cuts
.546
13.12.2
Acyclic Decompositions of Digraphs
.548
13.12.3
Decomposing Tournaments into Strong
Subtournaments
.548
13.12.4
Decomposing Digraphs under Degree Constraints
. 549
13.13
Exercises
.550
xx Contents
14.
Increasing
Connectivity.553
14.1 The Splitting Off Operation .553
14.2
Increasing the Arc-Strong Connectivity Optimally
.557
14.3
Increasing the Vertex-Strong Connectivity Optimally
.562
14.3.1
One-Way Pairs
.563
14.3.2
Optimal fc-Strong Augmentation
.565
14.3.3
Special Classes of Digraphs
.566
14.4
Arc Reversals and Vertex-Strong Connectivity
.568
14.5
Arc-Reversals and Arc-Strong Connectivity
.570
14.5.1
Determining rf9(D) Efficiently
.571
14.5.2
Reversals of Arcs to Achieve High Arc-Strong Connec¬
tivity in Tournaments
.572
14.6
Increasing Connectivity by Deorienting Arcs
.573
14.7
Miscellaneous Topics
.576
14.7.1
Increasing Arc-Strong Connectivity of a Bipartite Di¬
graph
.576
14.7.2
Augmenting Arc-Strong Connectivity in Directed Hy-
pergraphs
.577
14.7.3
Weighted Versions of Local Arc-Connectivity Problems
578
14.8
Exercises
.580
15.
Feedback Sets and Vertex
Orderings
.583
15.1
Two Conjectures on Feedback Arc Sets
.584
15.2
Optimal
Orderings
in Tournaments
.585
15.3
Complexity of the Feedback Set Problems
.586
15.3.1
jVP-Completeness Results
.587
15.3.2
FAS for Planar Digraphs
.590
15.3.3
Approximation Algorithms
.591
15.3.4
Fixed-Parameter Tractability Results
.593
15.4
Disjoint Cycles Versus Feedback Sets
.596
15.4.1
Relations Between Parameters
щ
and
r¿
.596
15.4.2
Solution of Youngers Conjecture
.598
15.5
Optimal
Orderings
and Seymour's Second Neighbourhood
Conjecture
.600
15.6
Adam's Conjecture
.603
15.7
Exercises
.605
16.
Generalizations of Digraphs: Edge-Coloured Multigraphs
. 607
16.1
Terminology, Notation and Initial Observations
.608
16.2
Properly Coloured
Euler
Trails
.610
16.3
Properly Coloured Cycles
.613
16.4
Gadget Graphs and Shortest PC Cycles and (s,i)-Paths
.617
16.4.1
P-Gadgets
.617
16.4.2
P-Gadget Graphs
.618
16.5
Long PC Cycles and Paths
.621
Contents xxi
16.6 Connectivity
of Edge-Coloured Multigraphs
.622
16.7
Alternating Cycles in 2-Edge-Coloured Bipartite Multigraphs
625
16.8
Paths and Cycles in 2-Edge-Coloured Complete Multigraphs
. 628
16.9
PC Paths and Cycles in c-Edge-Coloured Complete Graphs,
с
> 3 .635
16.10
Exercises
.640
17.
Applications of Digraphs and Edge-Coloured Graphs
.643
17.1
A Digraph Model in Quantum Mechanics
.643
17.1.1
Lower Bound for
μ(η)
.644
17.1.2
Families of Sets and
μ(η)
.644
17.1.3
Upper Bounds for
μ(η)
.646
17.1.4
When
μ(η)
>
f {n)
.647
17.1.5
Mediated Digraphs in Quantum Mechanics
.647
17.2
Embedded Computing and Convex Sets in Acyclic Digraphs
. 649
17.2.1
Embedded Computing Systems and Convex Sets
.649
17.2.2
Bounds for the Number of Convex Sets
.650
17.2.3
Algorithms for Generating Convex and Connected
Convex Sets
.652
17.3
When Greedy-Like Algorithms Fail
.655
17.3.1
Greedy Algorithm
.656
17.3.2
Max-Regret Algorithms
.659
17.4
Domination Analysis of ATSP Heuristics
.660
17.4.1
ATSP Heuristics with Factorial Domination Numbers
. 662
17.4.2
Upper Bounds on Domination Numbers
.664
17.5
Solving the 2-Satisfiability Problem
.666
17.6
Alternating Hamilton Cycles in Genetics
.670
17.6.1
Proof of Theorem
17.6.1.672
17.6.2
Proof of Theorem
17.6.2.673
17.7
Gaussian Elimination
.674
17.8
Markov Chains
.677
17.9
List Edge-Colourings
.679
17.10
Digraph Models of Bartering
.683
17.11
PERT/CPM in Project Scheduling
.685
17.12
Finite Automata
.687
17.13
Puzzles and Digraphs
.689
17.14
Gossip Problems
.690
17.15
Deadlocks of Computer Processes
.692
17.16
Exercises
.694
18.
Algorithms and Their Complexity
.695
18.1
Combinatorial Algorithms
.696
18.2
yVP-Complete and AfP-Hard Problems
.700
18.3
The Satisfiability Problem
.702
18.4
Fixed-Parameter Tractability and Intractability
.703
xxii Contents
18.5
Exponential Algorithms
.705
18.6
Approximation Algorithms
.706
18.7
Heuristics and Metaheuristics
.707
18.8
Matroids
.711
18.8.1
The Dual of a Matroid
.713
18.8.2
The Greedy Algorithm for Matroids
.714
18.8.3
Independence Oracles
.715
18.8.4
Union of Matroids
.715
18.8.5
Intersection of Two Matroids
.716
18.8.6
Intersections of Three or More Matroids
.717
18.9
Exercises
.717
References
.721
Symbol Index
.761
Author Index
.767
Subject Index
.777 |
| any_adam_object | 1 |
| author | Bang-Jensen, Jørgen 1960- Gutin, Gregory Z. 1957- |
| author_GND | (DE-588)142714992 (DE-588)142715557 |
| author_facet | Bang-Jensen, Jørgen 1960- Gutin, Gregory Z. 1957- |
| author_role | aut aut |
| author_sort | Bang-Jensen, Jørgen 1960- |
| author_variant | j b j jbj g z g gz gzg |
| building | Verbundindex |
| bvnumber | BV035403511 |
| callnumber-first | Q - Science |
| callnumber-label | QA166 |
| callnumber-raw | QA166.15 |
| callnumber-search | QA166.15 |
| callnumber-sort | QA 3166.15 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 890 ST 134 |
| ctrlnum | (OCoLC)299122758 (DE-599)DNB989847470 |
| dewey-full | 511/.54 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511/.54 |
| dewey-search | 511/.54 |
| dewey-sort | 3511 254 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV035403511 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-19T17:01:05Z |
| institution | BVB |
| isbn | 9780857290410 9781848009974 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017324117 |
| oclc_num | 299122758 |
| open_access_boolean | |
| owner | DE-20 DE-703 DE-11 DE-83 DE-29T DE-188 DE-634 DE-739 |
| owner_facet | DE-20 DE-703 DE-11 DE-83 DE-29T DE-188 DE-634 DE-739 |
| physical | XXII, 795 Seiten Diagramme |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer monographs in mathematics |
| spelling | Bang-Jensen, Jørgen 1960- Verfasser (DE-588)142714992 aut Digraphs theory, algorithms and applications Jørgen Bang-Jensen ; Gregory Gutin 2. ed. London [u.a.] Springer 2009 XXII, 795 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Springer monographs in mathematics Directed graphs Graphentheorie (DE-588)4113782-6 gnd rswk-swf Gerichteter Graph (DE-588)4156815-1 gnd rswk-swf Digraph (DE-588)4012307-8 gnd rswk-swf Komplexitätstheorie (DE-588)4120591-1 gnd rswk-swf Gerichteter Graph (DE-588)4156815-1 s Graphentheorie (DE-588)4113782-6 s Komplexitätstheorie (DE-588)4120591-1 s DE-604 Digraph (DE-588)4012307-8 s 1\p DE-604 Gutin, Gregory Z. 1957- Verfasser (DE-588)142715557 aut Erscheint auch als Online-Ausgabe 978-1-84800-998-1 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017324117&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bang-Jensen, Jørgen 1960- Gutin, Gregory Z. 1957- Digraphs theory, algorithms and applications Directed graphs Graphentheorie (DE-588)4113782-6 gnd Gerichteter Graph (DE-588)4156815-1 gnd Digraph (DE-588)4012307-8 gnd Komplexitätstheorie (DE-588)4120591-1 gnd |
| subject_GND | (DE-588)4113782-6 (DE-588)4156815-1 (DE-588)4012307-8 (DE-588)4120591-1 |
| title | Digraphs theory, algorithms and applications |
| title_auth | Digraphs theory, algorithms and applications |
| title_exact_search | Digraphs theory, algorithms and applications |
| title_full | Digraphs theory, algorithms and applications Jørgen Bang-Jensen ; Gregory Gutin |
| title_fullStr | Digraphs theory, algorithms and applications Jørgen Bang-Jensen ; Gregory Gutin |
| title_full_unstemmed | Digraphs theory, algorithms and applications Jørgen Bang-Jensen ; Gregory Gutin |
| title_short | Digraphs |
| title_sort | digraphs theory algorithms and applications |
| title_sub | theory, algorithms and applications |
| topic | Directed graphs Graphentheorie (DE-588)4113782-6 gnd Gerichteter Graph (DE-588)4156815-1 gnd Digraph (DE-588)4012307-8 gnd Komplexitätstheorie (DE-588)4120591-1 gnd |
| topic_facet | Directed graphs Graphentheorie Gerichteter Graph Digraph Komplexitätstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017324117&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT bangjensenjørgen digraphstheoryalgorithmsandapplications AT gutingregoryz digraphstheoryalgorithmsandapplications |