圖論導(dǎo)引

內(nèi)容概要

　　本書介紹了圖論的常用主題，同時也包含一些尚需進(jìn)一步研究或未解決的議題，用于激發(fā)學(xué)生的創(chuàng)新能力。全書共分13章，前3章介紹一些基礎(chǔ)知識，后面章節(jié)介紹了樹、連通性、可遍歷性、子圖、匹配和因子分解、可平面性、圖的著色、拉姆齊數(shù)、距離及控制等內(nèi)容。本書內(nèi)容全面，證明與應(yīng)用實(shí)例并舉，還給出了證明技巧，書的最后提供了奇數(shù)題號的解答或提示。    本書可作為本科生一學(xué)期課程教材，也可供圖論愛好者自學(xué)使用。

書籍目錄

1.　Introduction1.1.　Graphs and Graph Models  11.2.　Connected Graphs  91.3.　Common Classes of Graphs  191.4.　Multigraphs and Digraphs  262.　Degrees2.1.　The Degree of a Vertex  312.2.　Regular Graphs  382.3.　Degree Sequences  432.4.　Excursion:Graphs and Matrices  482.5.　Exploration:Irregular Graphs  503.　Isomorphic Graphs3.1.　The Definiition of Isomorphism  553.2.　Isomorphism as a Relation  633.3.　Excursion:Graphs and Groups  663.4.　Excursion:Reconstruction and Solvability  764.　Trees4.1.　Bridges  854.2.　Trees  874.3.　The Minimum Spanning Tree Problem  944.4.　Excursion:The Number of Spanning Trees  1015.　Connectivity5.1.　Cut-Vertices  1075.2.　Blocks  1115.3.　Connectivity  1155.4.　Menger's Theorem  1245.5.　Exploration:Geodetic Sets  1306.　Traversability6.1.　Eulerian Graphs  1336.2.　Hamiltonian Graphs  1406.3.　Exploration:Hamiltonian Walks and Numbers  1526.4.　Excursion:The Early Books of Graph Theory  1567.　Digraphs7.1.　Strong Digraphs  1617.2.　Tournaments  1697.3.　Excursion:Decision-Making  1767.4.　Exploration:Wine Bottle Problems  1808.　Matchings and Factorization8.1.　Matchings  1838.2.　Factorization  1948.3.　Decompositions and Graceful Labelings  2098.4.　Excursion:Instant Insanity  2148.5.　Excursion:The Petersen Graph  2198.6.　Exploration:γ-Labelings of Graphs  2249.　Planarity9.1.　Planar Graphs  2279.2.　Embedding Graphs on Surfaces  2419.3.　Excursion:Graph Minors  2499.4.　Exploration:Embedding Graphs in Graphs  25310.　Coloring10.1.　The Four Color Problem  25910.2.　Vertex Coloring  26710.3.　Edge Coloring  28010.4.　Excursion:The Heawood Map Coloring Theorem  28810.5.　Exploration:Local Coloring  29311.　Ramsey Numbers11.1.　The Ramsey Number of Graphs  29711.2.　Turan's Theorem  30711.3.　Exploration:Rainbow Ramsey Numbers  31411.4.　Excursion:Erdos Numbers  32112.　Distance12.1.　The Center of a Graph  32712.2.　Distant Vertices  33312.3.　Excursion:Locating Numbers  34112.4.　Excursion:Detour and Directed Distance  34612.5.　Exploration:Channel Assignment  35112.6.　Exploration:Distance Between Graphs  35713.　Domination13.1.　The Domination Number of a Graph  36113.2.　Exploration:Stratification  37213.3.　Exploration:Lights Out  37713.4.　Excursion:And Still It Grows More Colorful  381Solutions and Hints for Odd-Numbered Exercises  397References  425Index of Names  437Index of Mathematical Terms  440List of Symbols  447

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