Graph Theory: Modeling, Applications, and Algorithms (美國原版)

Description

For junior- to senior-level courses in Graph Theory taken by majors in Mathematics, Computer Science, or Engineering or for beginning-level graduate courses.

 

Once considered an “unimportant” branch of topology, graph theory has come into its own through many important contributions to a wide range of fields — and is now one of the fastest-growing areas in discrete mathematics and computer science. This new text introduces basic concepts, definitions, theorems, and examples from graph theory. The authors present a collection of interesting results from mathematics that involve key concepts and proof techniques; cover design and analysis of computer algorithms for solving problems in graph theory; and discuss applications of graph theory to the sciences. It is mathematically rigorous, but also practical, intuitive, and algorithmic.

 

 

 

Table of Contents

Preface                                                                                                     

1     Introduction to Graph Theory                                               

2     Basic Concepts in Graph Theory                                      

3     TreesandForests

4     Spanning Trees

5     Fundamental Properties of Graphs and Digraphs

6     Connectivity and Flow

7     Planar Graphs

8     Graph Coloring

9     Coloring Enumerations and Chordal Graphs

10    Independence,Dominance, and Matchings  

11    Cover Parameters and MatchingPolynomials

12    GraphCounting

13    Graph Algorithms

 

APPENDICES

A Greek Alphabet

B Notation

C Top Ten Online References

Index ix

描述

這本新書介紹了圖論的基本概念、定義、定理和例子。作者們介紹了數學中涉及關鍵概念和證明技巧的一系列有趣結果；涵蓋了設計和分析解決圖論問題的計算機算法；並討論了圖論在科學中的應用。這本書在數學上是嚴謹的，但也是實用的、直觀的和算法的。

目錄

前言
1. 圖論介紹
2. 圖論的基本概念
3. 樹和森林
4. 生成樹
5. 圖和有向圖的基本性質
6. 連通性和流
7. 平面圖
8. 圖的著色
9. 著色枚舉和弦圖