圖論導(dǎo)引

內(nèi)容概要

　　圖論在計(jì)算科學(xué)、社會科學(xué)和自然科學(xué)等各個(gè)領(lǐng)域都有廣泛應(yīng)用。本書是本科生或研究生一學(xué)期或兩學(xué)期的圖論課程教材。全書力求保持按證明的難度和算法的復(fù)雜性循序漸進(jìn)的風(fēng)格，使學(xué)生能夠深入理解書中的內(nèi)容。書中包括對證明技巧的討論、1200多道習(xí)題、400多幅插圖以及許多例題，而且對所有定理都給出了詳細(xì)完整的證明。雖然本書包括許多算法和應(yīng)用，但是重點(diǎn)在于理解圖論結(jié)構(gòu)和分析圖論問題的技巧。

書籍目錄

PrefaceChapter 1 Fundamental Concepts  1.1 What Is a Graph?    The Definition    Graphs as Models    Matrices and Ismorphism    Decomposition and Special Graphs     Exercises  1.2 Paths,Cycles,and Trails    Connection in Graphs     Bipartite Graphs    Exercises  1.3 Vertex Degrees and Counting    Counting and Bijections     Extremal Problems    Graphic Sequences    Excercises  1.4 Directed Graphs     Definitions and Examples    Vertex Degrees  Eulerian Digraphs    Orientations and Tournaments    ExercisesChapter 2 Trees and Distance  2.1 Basic Properties    Properties of Trees    Distance in Trees and Graphs    Disjoint Spanning Trees(optional)    Exercises  2.2 Spanning Trees and Enumeration    Enumeration of Trees    Spanning Trees in Graphs    Decomposition and Graceful Labelings    Branchings and Eulerian Digraphs(optional)  2.3 Optimization and Trees    Minimum Spanning Tree    Shortese Paths    Trees in Computer Science(optional)    ExercisesChapter 3 Matchings and Factors  3.1 Matchings and Covers    Maximum Matchings     Hall's Matching Condition    Min-Max Theorems    Independent Sets and Covers    Dominating Sets(optional)    Exercises  3.2 Algorithms and Applications    Maximum Bipartite Matching    Weighted Bipartite Matching    Stable Matchings(optional)    Faster Bipartite Matching(optional)    Exercises  3.3 Matchings in General Graphs    Tutt's 1-factor Hteorem    f-factors of Graphs(optional)    Edmonds'Blossom Algorithm(optional)    Exercises……Chapter 4 Connectivity and PathsChapter 5 Coloing of GraphsChapter 6 Planar GraphsChapter 7 Edges and CyclesChapter 8 Additional Topics(optional)Appendix A Mathematical BackgroundAppendix B Optimization and ComplexityAppendix C Hints for Selected ExercisesAppendix D Glossary of TermsAppendix E Supplemental ReaningAppendix F ReferencesAuthor IndexSubject Index

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