Graphs & Digraphs

NOTE EDITORE

Graphs & Digraphs masterfully employs student-friendly exposition, clear proofs, abundant examples, and numerous exercises to provide an essential understanding of the concepts, theorems, history, and applications of graph theory. Fully updated and thoughtfully reorganized to make reading and locating material easier for instructors and students, the Sixth Edition of this bestselling, classroom-tested text: Adds more than 160 new exercises Presents many new concepts, theorems, and examples Includes recent major contributions to long-standing conjectures such as the Hamiltonian Factorization Conjecture, 1-Factorization Conjecture, and Alspach’s Conjecture on graph decompositions Supplies a proof of the perfect graph theorem Features a revised chapter on the probabilistic method in graph theory with many results integrated throughout the text At the end of the book are indices and lists of mathematicians’ names, terms, symbols, and useful references. There is also a section giving hints and solutions to all odd-numbered exercises. A complete solutions manual is available with qualifying course adoption. Graphs & Digraphs, Sixth Edition remains the consummate text for an advanced undergraduate level or introductory graduate level course or two-semester sequence on graph theory, exploring the subject’s fascinating history while covering a host of interesting problems and diverse applications.

SOMMARIO

IntroductionGraphsThe Degree of a VertexIsomorphic GraphsRegular GraphsBipartite GraphsOperations on GraphsDegree SequencesMultigraphsExercises for Chapter 1 Connected Graphs and DistanceConnected GraphsDistance in GraphsExercises for Chapter 2 TreesNonseparable GraphsIntroduction to TreesSpanning TreesThe Minimum Spanning Tree ProblemExercises for Chapter 3 ConnectivityConnectivity and Edge-ConnectivityTheorems of Menger and WhitneyExercises for Chapter 4 Eulerian GraphsThe Königsberg Bridge ProblemEulerian Circuits and TrailsExercises for Chapter 5 Hamiltonian GraphsHamilton's Icosian GameSufficient Conditions for HamiltonicityToughness of GraphsHighly Hamiltonian GraphsPowers of Graphs and Line GraphsExercises for Chapter 6 DigraphsIntroduction to DigraphsStrong DigraphsEulerian and Hamiltonian DigraphsTournamentsKings in TournamentsHamiltonian TournamentsExercises for Chapter 7 Flows in NetworksNetworksThe Max-Flow Min-Cut TheoremMenger Theorems for DigraphsExercises for Chapter 8 Automorphisms and ReconstructionThe Automorphism Group of a GraphCayley Color GraphsThe Reconstruction ProblemExercises for Chapter 9 Planar GraphsThe Euler IdentityMaximal Planar GraphsCharacterizations of Planar GraphsHamiltonian Planar GraphsExercises for Chapter 10 Nonplanar GraphsThe Crossing Number of a GraphThe Genus of a GraphThe Graph Minor TheoremExercises for Chapter 11 Matchings, Independence and DominationMatchings1-FactorsIndependence and CoversDominationExercises for Chapter 12 Factorization and DecompositionFactorizationDecompositionCycle DecompositionGraceful GraphsExercises for Chapter 13 Vertex ColoringsThe Chromatic Number of a GraphColor-Critical GraphsBounds for the Chromatic NumberExercises for Chapter 14 Perfect Graphs and List ColoringsPerfect GraphsThe Perfect and Strong Perfect Graph TheoremsList ColoringsExercises for Chapter 15 Map ColoringsThe Four Color ProblemColorings of Planar GraphsList Colorings of Planar GraphsThe Conjectures of Hajós and HadwigerChromatic PolynomialsThe Heawood Map-Coloring ProblemExercises for Chapter 16 Edge ColoringsThe Chromatic Index of a GraphClass One and Class Two GraphsTait ColoringsExercises for Chapter 17 Nowhere-Zero Flows, List Edge ColoringsNowhere-Zero FlowsList Edge ColoringsTotal ColoringsExercises for Chapter 18 Extremal Graph TheoryTurán's TheoremExtremal SubgraphsCagesExercises for Chapter 19 Ramsey TheoryClassical Ramsey NumbersMore General Ramsey NumbersExercises for Chapter 20 The Probabilistic MethodThe Probabilistic MethodRandom GraphsExercises for Chapter 21 Hints and Solutions to Odd-Numbered Exercises Bibliography Supplemental References Index of Names Index of Mathematical Terms List of Symbols

AUTORE

Gary Chartrand is a professor emeritus of mathematics at Western Michigan University, Kalamazoo, Michigan, USA. Linda Lesniak, a professor emeritus of mathematics from Drew University, Madison, New Jersey, USA, is currently a visiting mathematician at Western Michigan University, Kalamazoo, Michigan, USA. Ping Zhang is a professor of mathematics at Western Michigan University, Kalamazoo, Michigan, USA. All three have authored or coauthored many textbooks in mathematics and numerous research articles in graph theory.

ALTRE INFORMAZIONI

• Condizione: Nuovo
• ISBN: 9781498735766
• Collana: Discrete Mathematics and Its Applications
• Dimensioni: 9.25 x 6.25 in Ø 2.30 lb
• Formato: Copertina rigida
• Illustration Notes: 343 b/w images
• Pagine Arabe: 640