Topics in Graph Theory

The interplay between graph theory and a wide variety of models and applications in mathematics, computer science, operations research, and the natural and social sciences continues to grow.

This book is geared toward the more mathematically mature student. The first two chapters provide the basic definitions and theorems of graph theory and the remaining chapters introduce a variety of topics and directions for research. These topics draw on numerous areas of theoretical and applied mathematics, including combinatorics, probability, linear algebra, group theory, topology, operations research, and computer science. This makes the book appropriate for a first course at the graduate level or as a second course at the undergraduate level.

The authors build upon material previously published in Graph Theory and Its Applications, third edition, by the same authors. That text covers material for both an undergraduate and graduate course, while this book builds on and expands the graduate-level material.

List of Features

• Extensive exercises and applications.
• Flexibility: appropriate for either a first course at the graduate level; or an advanced course at the undergraduate level.
• Opens avenues to a variety of research areas in graph theory.
• Emphasis on topological and algebraic graph theory

圖論與數學、計算機科學、運籌學以及自然科學和社會科學中各種模型和應用之間的相互作用不斷增長。

本書針對數學基礎較為成熟的學生。前兩章介紹了圖論的基本定義和定理，其餘章節介紹了各種主題和研究方向。這些主題涉及了許多理論和應用數學領域，包括組合學、概率論、線性代數、群論、拓撲學、運籌學和計算機科學。這使得本書適合研究生的第一門課程或本科的第二門課程。

作者們在之前出版的同名書籍《圖論及其應用》第三版的基礎上進一步擴充了研究生級別的內容。

特點列表:
- 大量的練習和應用。
- 靈活性：適合研究生的第一門課程或本科的高級課程。
- 開拓了圖論的各種研究領域。
- 強調拓撲和代數圖論。

Mark Anderson is a professor of mathematics and computer science at Rollins College. His research interests in graph theory center on the topological or algebraic side.

Jonathan L. Gross

is a professor of computer science at Columbia University. His research interests include topology and graph theory.

Jay Yellen is a professor of mathematics at Rollins College. His current areas of research include graph theory, combinatorics, and algorithms.

Mark Anderson是Rollins College的數學和計算機科學教授。他在圖論方面的研究興趣集中在拓撲或代數方面。

Jonathan L. Gross是哥倫比亞大學的計算機科學教授。他的研究興趣包括拓撲和圖論。

Jay Yellen是Rollins College的數學教授。他目前的研究領域包括圖論、組合數學和算法。