Graph Theory

A lively invitation to the flavor, elegance, and power of graph theory This mathematically rigorous introduction is tempered and enlivened by numerous illustrations, revealing examples, seductive applications, and historical references. An award-winning teacher, Russ Merris has crafted a book designed to attract and engage through its spirited exposition, a rich assortment of well-chosen exercises, and a selection of topics that emphasizes the kinds of things that can be manipulated, counted, and pictured. Intended neither to be a comprehensive overview nor an encyclopedic reference, this focused treatment goes deeply enough into a sufficiently wide variety of topics to illustrate the flavor, elegance, and power of graph theory. Another unique feature of the book is its user-friendly modular format. Following a basic foundation in Chapters 1-3, the remainder of the book is organized into four strands that can be explored independently of each other. These strands center, respectively, around matching theory; planar graphs and hamiltonian cycles; topics involving chordal graphs and oriented graphs that naturally emerge from recent developments in the theory of graphic sequences; and an edge coloring strand that embraces both Ramsey theory and a self-contained introduction to Pólya's enumeration of nonisomorphic graphs. In the edge coloring strand, the reader is presumed to be familiar with the disjoint cycle factorization of a permutation. Otherwise, all prerequisites for the book can be found in a standard sophomore course in linear algebra. The independence of strands also makes Graph Theory an excellent resource for mathematicians who require access to specific topics without wanting to read an entire book on the subject.