ENGLISH

Chromatic graph theory

By Gary Chartrand; Ping Zhang

Book information

Year
2020
ISBN
9781138343863, 1138343862
Language
english
Format
PDF
Filesize
14 MB (14654770 bytes)
Series
A Chapman & Hall book
Edition
Second
Pages
\526
Time added
2020-09-11 02:12:50

Description

Cover Half Title Title Page Copyright Page Dedication Table of Contents PREFACE TO THE SECOND EDITION List of Symbols 0: The Origin of Graph Colorings 1: Introduction to Graphs 1.1 Fundamental Terminology 1.2 Connected Graphs 1.3 Distance in Graphs 1.4 Isomorphic Graphs 1.5 Common Graphs and Graph Operations 1.6 Multigraphs and Digraphs Exercises for Chapter 1 2: Trees and Connectivity 2.1 Cut-Vertices, Bridges, and Blocks 2.2 Trees 2.3 Connectivity and Edge-Connectivity 2.4 Menger's Theorem Exercises for Chapter 2 3: Eulerian and Hamiltonian Graphs 3.1 Eulerian Graphs 3.2 de Bruijn Digraphs 3.3 Hamiltonian Graphs Exercises for Chapter 3 4: Matchings and Factorization 4.1 Matchings and Independence 4.2 Factorization and Decomposition Exercises for Chapter 4 5: Graph Embeddings 5.1 Planar Graphs and the Euler Identity 5.2 Hamiltonian Planar Graphs 5.3 Planarity versus Nonplanarity 5.4 Outerplanar Graphs 5.5 Embedding Graphs on Surfaces 5.6 The Graph Minor Theorem Exercises for Chapter 5 6: Introduction to Vertex Colorings 6.1 The Chromatic Number of a Graph 6.2 Applications of Colorings 6.3 Perfect Graphs Exercises for Chapter 6 7: Bounds for the Chromatic Number 7.1 Color-Critical Graphs 7.2 Upper Bounds and Greedy Colorings 7.3 Upper Bounds and Oriented Graphs 7.4 The Chromatic Number of Cartesian Products Exercises for Chapter 7 8: Coloring Graphs on Surfaces 8.1 The Four Color Problem 8.2 The Conjectures of Hajós and Hadwiger 8.3 Chromatic Polynomials 8.4 The Heawood Map-Coloring Problem Exercises for Chapter 8 9: Restricted Vertex Colorings 9.1 Uniquely Colorable Graphs 9.2 List Colorings 9.3 Precoloring Extensions of Graphs Exercises for Chapter 9 10: Edge Colorings 10.1 The Chromatic Index and Vizing's Theorem 10.2 Class One and Class Two Graphs 10.3 Tait Colorings 10.4 Nowhere-Zero Flows 10.5 List Edge Colorings 10.6 Total Colorings of Graphs Exercises for Chapter 10 11: Ramsey Theory 11.1 Ramsey Numbers 11.2 Bipartite Ramsey Numbers 11.3 s-Bipartite Ramsey Numbers Exercises for Chapter 11 12: Monochromatic Ramsey Theory 12.1 Monochromatic Ramsey Numbers 12.2 Monochromatic-Bichromatic Ramsey Numbers 12.3 Proper Ramsey Numbers 12.4 Rainbow Ramsey Numbers 12.5 Gallai-Ramsey Numbers Exercises for Chapter 12 13: Color Connection 13.1 Rainbow Connection 13.2 Proper Connection 13.3 Rainbow Disconnection Exercises for Chapter 13 14: Distance and Colorings 14.1 T-Colorings 14.2 L(2; 1)-Colorings 14.3 Radio Colorings 14.4 Hamiltonian Colorings Exercises for Chapter 14 15: Domination and Colorings 15.1 Domination Parameters 15.2 Stratified Domination 15.3 Domination Based on K3-Colorings 15.4 Stratified Domination by Multiple Graphs Exercises for Chapter 15 16: Induced Colorings 16.1 Majestic Colorings 16.2 Royal and Regal Colorings 16.3 Rainbow Mean Colorings Exercises for Chapter 16 17: The Four Color Theorem Revisited 17.1 Zonal Labelings of Planar Graphs 17.2 Zonal Labelings and Edge Colorings Exercises for Chapter 17 Bibliography Index (Names and Mathematical Terms)

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