Digraphs : Theory, Algorithms and Applications,9781852332686

Digraphs : Theory, Algorithms and Applications

by ;
ISBN13: 9781852332686
ISBN10: 1852332689
Format: Hardcover
Pub. Date: 2000-12-01
Publisher(s): Springer Verlag
  • Free Shipping Icon

    This Item Qualifies for Free Shipping!*

    *Excludes marketplace orders.

List Price: $109.20

Rent Textbook

Select for Price
Add to Cart
There was a problem. Please try again later.

Rent Digital

Rent Digital Options
Online:30 Days access
Downloadable:30 Days
$35.64
Online:60 Days access
Downloadable:60 Days
$47.52
Online:90 Days access
Downloadable:90 Days
$59.40
Online:120 Days access
Downloadable:120 Days
$71.28
Online:180 Days access
Downloadable:180 Days
$77.22
Online:1825 Days access
Downloadable:Lifetime Access
$118.80
$77.22
Add to Cart

New Textbook

We're Sorry
Sold Out

Used Textbook

We're Sorry
Sold Out

Buy from our Marketplace starting at $87.21

How Marketplace Works:

  • This item is offered by an independent seller and not shipped from our warehouse
  • Item details like edition and cover design may differ from our description; see seller's comments before ordering.
  • Sellers much confirm and ship within two business days; otherwise, the order will be cancelled and refunded.
  • Marketplace purchases cannot be returned to eCampus.com. Contact the seller directly for inquiries; if no response within two days, contact customer service.
  • Additional shipping costs apply to Marketplace purchases. Review shipping costs at checkout.

Summary

The study of directed graphs has developed enormously over recent decades, yet no book covers more than a tiny fraction of the results from more than 3000 research articles on the topic. Digraphsis the first book to present a unified and comprehensive survey of the subject. In addition to covering the theoretical aspects, including detailed proofs of many important results, the authors present a number of algorithms and applications. The applications of digraphs and their generalizations include among other things recent developments in the Travelling Salesman Problem, genetics and network connectivity. More than 700 exercises and 180 figures will help readers to study the topic while open problems and conjectures will inspire further research. This book will be essential reading and reference for all graduate students, researchers and professionals in mathematics, operational research, computer science and other areas who are interested in graph theory and its applications.

Author Biography

Jorgen Bang-Jensen is associate Professor in the Department of Mathematics and Computer Science at the University of Southern Denmark, Odense, Denmark Gregory Gutin is Professor of Computer Science at Royal Holloway College, University of London

Table of Contents

Basic Terminology, Natation and Results
1(44)
Sets, Subsets, Matrices and Vectors
1(1)
Digraphs, Subdigraphs, Neighbours, Degrees
2(4)
Isomorphism and Basic Operations on Digraphs
6(4)
Walks, Trails, Paths, Cycles and Path-Cycle Subdigraphs
10(6)
Strong and Unilateral Connectivity
16(2)
Undirected Graphs, Biorientations and Orientations
18(4)
Mixed Graphs and Hypergraphs
22(3)
Classes of Directed and Undirected Graphs
25(3)
Algorithmic Aspects
28(7)
Algorithms and their Complexity
29(4)
NP-Complete and NP-Hard Problems
33(2)
Application: Solving the 2-Satisfiability Problem
35(3)
Exercises
38(7)
Distances
45(50)
Terminology and Notation on Distances
46(2)
Structure of Shortest Paths
48(2)
Algorithms for Finding Distances in Digraphs
50(9)
Breadth-First Search (BFS)
50(2)
Acyclic Digraphs
52(1)
Dijkstra's Algorithm
53(2)
The Bellman-Ford-Moore Algorithm
55(3)
The Floyd-Warshall Algorithm
58(1)
Inequalities Between Radius, Out-Radius and Diameter
59(2)
Radius and Diameter of a Strong Digraph
59(1)
Extreme Values of Out-Radius and Diameter
60(1)
Maximum Finite Diameter of Orientations
61(2)
Minimum Diameter of Orientations of Multigraphs
63(4)
Minimum Diameter Orientations of Complete Multipartite Graphs
67(2)
Minimum Diameter Orientations of Extensions of Graphs
69(2)
Minimum Diameter Orientations of Cartesian Products of Graphs
71(3)
Kings in Digraphs
74(4)
2-Kings in Tournaments
74(1)
Kings in Semicomplete Multipartite Digraphs
75(3)
Kings in Generalizations of Tournaments
78(1)
Application: The One-Way Street and the Gossip Problems
78(4)
The One-Way Street Problem and Orientations of Digraphs
79(1)
The Gossip Problem
80(2)
Application: Exponential Neighbourhood Local Search for the TSP
82(7)
Local Search for the TSP
82(2)
Linear Time Searchable Exponential Neighbourhoods for the TSP
84(1)
The Assignment Neighbourhoods
85(1)
Diameters of Neighbourhood Structure Digraphs for the TSP
86(3)
Exercises
89(6)
Flows in Networks
95(76)
Definitions and Basic Properties
95(4)
Flows and Their Balance Vectors
96(2)
The Residual Network
98(1)
Reductions Among Different Flow Models
99(5)
Eliminating Lower Bounds
99(1)
Flows with one Source and one Sink
100(1)
Circulations
101(1)
Networks with Bounds and Costs on the Vertices
102(2)
Flow Decompositions
104(1)
Working with the Residual Network
105(3)
The Maximum Flow Problem
108(6)
The Ford-Fulkerson Algorithm
110(3)
Maximum Flows and Linear Programming
113(1)
Polynomial Algorithms for Finding a Maximum (s,t)-Flow
114(8)
Flow Augmentations Along Shortest Augmenting Paths
114(2)
Blocking Flows in Layered Networks and Dinic's Algorithm
116(1)
The Preflow-Push Algorithm
117(5)
Unit Capacity Networks and Simple Networks
122(3)
Unit Capacity Networks
122(2)
Simple Networks
124(1)
Circulations and Feasible Flows
125(2)
Minimum Value Feasible (s,t)-Flows
127(1)
Minimum Cost Flows
128(9)
Characterizing Minimum Cost Flows
131(3)
Building up an Optimal Solution
134(3)
Applications of Flows
137(10)
Maximum Matchings in Bipartite Graphs
137(4)
The Directed Chinese Postman Problem
141(1)
Finding Subdigraphs with Prescribed Degrees
142(1)
Path-Cycle Factors in Directed Multigraphs
143(2)
Cycle Subdigraphs Covering Specified Vertices
145(2)
The Assignment Problem and the Transportation Problem
147(11)
Exercises
158(13)
Classes of Digraphs
171(56)
Depth-First Search
172(3)
Acyclic Orderings of the Vertices in Acyclic Digraphs
175(1)
Transitive Digraphs, Transitive Closures and Reductions
176(3)
Strong Digraphs
179(3)
Line Digraphs
182(5)
The de Bruijn and Kautz Digraphs and their Generalizations
187(4)
Series-Parallel Digraphs
191(4)
Quasi-Transitive Digraphs
195(3)
The Path-Merging Property and Path-Mergeable Digraphs
198(2)
Locally In-Semicomplete and Locally Out-Semicomplete Digraphs
200(2)
Locally Semicomplete Digraphs
202(13)
Round Digraphs
203(4)
Non-Strong Locally Semicomplete Digraphs
207(2)
Strong Round Decomposable Locally Semicomplete Digraphs
209(2)
Classification of Locally Semicomplete Digraphs
211(4)
Totally φi-Decomposable Digraphs
215(2)
Intersection Digraphs
217(2)
Planar Digraphs
219(2)
Application: Gaussian Elimination
221(3)
Exercises
224(3)
Hamiltonicity and Related Problems
227(54)
Necessary Conditions for Hamiltonicity of Digraphs
229(5)
Path-Contraction
229(1)
Quasi-Hamiltonicity
230(2)
Pseudo-Hamiltonicity and 1-Quasi-Hamiltonicity
232(1)
Algorithms for Pseudo- and Quasi-Hamiltonicity
233(1)
Path Covering Number
234(1)
Path Factors of Acyclic Digraphs with Applications
235(2)
Hamilton Paths and Cycles in Path-Mergeable Digraphs
237(1)
Hamilton Paths and Cycles in Locally In-Semicomplete Digraphs
238(2)
Hamilton Cycles and Paths in Degree-Constrained Digraphs
240(10)
Sufficient Conditions
240(6)
The Multi-Insertion Technique
246(2)
Proofs of Theorems 5.6.1 and 5.6.5
248(2)
Longest Paths and Cycles in Semicomplete Multipartite Digraphs
250(14)
Basic Results
251(2)
The Good Cycle Factor Theorem
253(3)
Consequences of Lemma 5.7.12
256(3)
Yeo's Irreducible Cycle Subdigraph Theorem and its Applications
259(5)
Longest Paths and Cycles in Extended Locally Semicomplete Digraphs
264(1)
Hamilton Paths and Cycles in Quasi-Transitive Digraphs
265(4)
Vertex-Heaviest Paths and Cycles in Quasi-Transitive Digraphs
269(4)
Hamilton Paths and Cycles in Various Classes of Digraphs
273(3)
Exercises
276(5)
Hamiltonian Refinements
281(64)
Hamiltonian Paths with a Prescribed End-Vertex
282(2)
Weakly Hamiltonian-Connected Digraphs
284(8)
Results for Extended Tournaments
284(5)
Results for Locally Semicomplete Digraphs
289(3)
Hamiltonian-Connected Digraphs
292(3)
Finding a Hamiltonian (x,y)-Path in a Semicomplete Digraph
295(4)
Pancyclicity of Digraphs
299(10)
(Vertex-) Pancyclicity in Degree-Constrained Digraphs
299(1)
Pancyclicity in Extended Semicomplete and Quasi-Transitive Digraphs
300(3)
Pancyclic and Vertex-Pancyclic Locally Semicomplete Digraphs
303(3)
Further Pancyclicity Results
306(2)
Cycle Extendability in Digraphs
308(1)
Arc-Pancyclicity
309(3)
Hamiltonian Cycles Containing or Avoiding Prescribed Arcs
312(6)
Hamiltonian Cycles Containing Prescribed Arcs
312(3)
Avoiding Prescribed Arcs with a Hamiltonian Cycle
315(2)
Hamiltonian Cycles Avoiding Arcs in 2-Cycles
317(1)
Arc-Disjoint Hamiltonian Paths and Cycles
318(3)
Oriented Hamiltonian Paths and Cycles
321(5)
Covering All Vertices of a Digraph by Few Cycles
326(5)
Cycle Factors with a Fixed Number of Cycles
326(3)
The Effect of α(D) on Spanning Configurations of Paths and Cycles
329(2)
Minimum Strong Spanning Subdigraphs
331(6)
A Lower Bound for General Digraphs
331(1)
The MSSS Problem for Extended Semicomplete Digraphs
332(2)
The MSSS Problem for Quasi-Transitive Digraphs
334(1)
The MSSS Problem for Decomposable Digraphs
335(2)
Application: Domination Number of TSP Heuristics
337(2)
Exercises
339(6)
Global Connectivity
345(70)
Additional Notation and Preliminaries
346(3)
The Network Representation of a Directed Multigraph
348(1)
Ear Decompositions
349(4)
Menger's Theorem
353(2)
Application: Determining Arc-and Vertex-Strong Connectivity
355(3)
The Splitting off Operation
358(4)
Increasing the Arc-Strong Connectivity Optimally
362(5)
Increasing the Vertex-Strong Connectivity Optimally
367(9)
One-Way Pairs
368(2)
Optimal k-Strong Augmentation
370(1)
Special Classes of Digraphs
371(2)
Splittings Preserving k-Strong Connectivity
373(3)
A Generalization of Arc-Strong Connectivity
376(2)
Arc Reversals and Vertex-Strong Connectivity
378(3)
Minimally k-(Arc)-Strong Directed Multigraphs
381(10)
Minimally k-Arc-Strong Directed Multigraphs
382(5)
Minimally k-Strong Digraphs
387(4)
Critically k-Strong Digraphs
391(1)
Arc-Strong Connectivity and Minimum Degree
392(1)
Connectivity Properties of Special Classes of Digraphs
393(2)
Highly Connected Orientations of Digraphs
395(5)
Packing Cuts
400(4)
Application: Small Certificates for k-(Arc)-Strong Connectivity
404(5)
Finding Small Certificates for Strong Connectivity
405(1)
Finding k-Strong Certificates for k > 1
406(2)
Certificates for k-Arc-Strong Connectivity
408(1)
Exercises
409(6)
Orientations of Graphs
415(60)
Underlying Graphs of Various Classes of Digraphs
415(14)
Underlying Graphs of Transitive and Quasi-Transitive Digraphs
416(3)
Underlying Graphs of Locally Semicomplete Digraphs
419(2)
Local Tournament Orientations of Proper Circular Arc Graphs
421(3)
Underlying Graphs of Locally In-Semicomplete Digraphs
424(5)
Fast Recognition of Locally Semicomplete Digraphs
429(3)
Orientations With no Even Cycles
432(3)
Colourings and Orientations of Graphs
435(2)
Orientations and Nowhere Zero Integer Flows
437(6)
Orientations Achieving High Arc-Strong Connectivity
443(3)
Orientations Respecting Degree Constraints
446(5)
Orientations with Prescribed Degree Sequences
446(4)
Restrictions on Subsets of Vertices
450(1)
Submodular Flows
451(11)
Submodular Flow Models
452(1)
Existence of Feasible Submodular Flows
453(4)
Minimum Cost Submodular Flows
457(1)
Applications of Submodular Flows
458(4)
Orientations of Mixed Graphs
462(5)
Exercises
467(8)
Disjoint Paths and Trees
475(70)
Additional Definitions
476(1)
Disjoint Path Problems
477(10)
The Complexity of the k-Path Problem
478(4)
Sufficient Conditions for a Digraph to be k-Linked
482(2)
The k-Path Problem for Acyclic Digraphs
484(3)
Linkings in Tournaments and Generalizations of Tournaments
487(10)
Sufficient Conditions in Terms of (Local-) Connectivity
488(4)
The 2-Path Problem for Semicomplete Digraphs
492(1)
The 2-Path Problem for Generalizations of Tournaments
493(4)
Linkings in Planar Digraphs
497(3)
Arc-Disjoint Branchings
500(6)
Implications of Edmonds' Branching Theorem
503(3)
Edge-Disjoint Mixed Branchings
506(1)
Arc-Disjoint Path Problems
507(13)
Arc-Disjoint Paths in Acyclic Directed Multigraphs
510(1)
Arc-Disjoint Paths in Eulerian Directed Multigraphs
511(6)
Arc-Disjoint Paths in Tournaments and Generalizations of Tournaments
517(3)
Integer Multicommodity Flows
520(2)
Arc-Disjoint In-and Out-Branchings
522(5)
Minimum Cost Branchings
527(9)
Matroid Intersection Formulation
527(1)
An Algorithm for a Generalization of the Min Cost Branching Problem
528(7)
The Minimum Covering Arborescence Problem
535(1)
Increasing Rooted Arc-Strong Connectivity by Adding New Arcs
536(2)
Exercises
538(7)
Cycle Structure of Digraphs
545(46)
Vector Spaces of Digraphs
546(3)
Polynomial Algorithms for Paths and Cycles
549(4)
Disjoint Cycles and Feedback Sets
553(8)
Complexity of the Disjoint Cycle and Feedback Set Problems
553(1)
Disjoint Cycles in Digraphs with Minimum Out-Degree at Least k
554(3)
Feedback Sets and Linear Orderings in Digraphs
557(4)
Disjoint Cycles Versus Feedback Sets
561(4)
Relations Between Parameters vi and Ti
561(2)
Solution of Younger's Conjecture
563(2)
Application: The Period of Markov Chains
565(2)
Cycles of Length k Modulo p
567(6)
Complexity of the Existence of Cycles of Length k Modulo p Problems
568(2)
Sufficient Conditions for the Existence of Cycles of Length k Modulo p
570(3)
`Short' Cycles in Semicomplete Multipartite Digraphs
573(4)
Cycles Versus Paths in Semicomplete Multipartite Digraphs
577(3)
Girth
580(3)
Additional Topics on Cycles
583(3)
Chords of Cycles
583(1)
Adam's Conjecture
584(2)
Exercises
586(5)
Generalizations of Digraphs
591(48)
Properly Coloured Trails in Edge-Coloured Multigraphs
592(28)
Properly Coloured Euler Trails
594(3)
Properly Coloured Cycles
597(4)
Connectivity of Edge-Coloured Multigraphs
601(3)
Alternating Cycles in 2-Edge-Coloured Bipartite Multigraphs
604(3)
Longest Alternating Paths and Cycles in 2-Edge-Coloured Complete Multigraphs
607(6)
Properly Coloured Hamiltonian Paths in c-Edge-Coloured Complete Graphs, c ⪈ 3
613(2)
Properly Coloured Hamiltonian Cycles in c-Edge-Coloured Complete Graphs, c ⪈ 3
615(5)
Arc-Coloured Directed Multigraphs
620(7)
Complexity of the Alternating Directed Cycle Problem
621(3)
The Functions f(n) and g(n)
624(2)
Weakly Eulerian Arc-Coloured Directed Multigraphs
626(1)
Hypertournaments
627(5)
Out-Degree Sequences of Hypertournaments
628(1)
Hamilton Paths
629(1)
Hamilton Cycles
630(2)
Application: Alternating Hamilton Cycles in Genetics
632(4)
Proof of Theorem 11.4.1
634(1)
Proof of Theorem 11.4.2
635(1)
Exercises
636(3)
Additional Topics
639(44)
Seymour's Second Neighbourhood Conjecture
639(3)
Ordering the Vertices of a Digraph of Paired Comparisons
642(8)
Paired Comparison Digraphs
642(3)
The Kano-Sakamoto Methods of Ordering
645(1)
Orderings for Semicomplete PCDs
645(1)
The Mutual Orderings
646(1)
Complexity and Algorithms for Forward and Backward Orderings
647(3)
(k, l)-Kernels
650(4)
Kernels
650(3)
Quasi-Kernels
653(1)
List Edge-Colourings of Complete Bipartite Graphs
654(4)
Homomorphisms-A Generalization of Colourings
658(6)
Other Measures of Independence in Digraphs
664(1)
Matroids
665(8)
The Dual of a Matroid
667(1)
The Greedy Algorithm for Matroids
668(1)
Independence Oracles
669(1)
Union of Matroids
670(1)
Two Matroid Intersection
671(1)
Intersections of Three or More Matroids
672(1)
Finding Good Solutions of NP-Hard Problems
673(4)
Exercises
677(6)
References 683(34)
Symbol Index 717(6)
Author Index 723(8)
Subject Index 731

An electronic version of this book is available through VitalSource.

This book is viewable on PC, Mac, iPhone, iPad, iPod Touch, and most smartphones.

By purchasing, you will be able to view this book online, as well as download it, for the chosen number of days.

Digital License

You are licensing a digital product for a set duration. Durations are set forth in the product description, with "Lifetime" typically meaning five (5) years of online access and permanent download to a supported device. All licenses are non-transferable.

More details can be found here.

A downloadable version of this book is available through the eCampus Reader or compatible Adobe readers.

Applications are available on iOS, Android, PC, Mac, and Windows Mobile platforms.

Please view the compatibility matrix prior to purchase.