Graph Theory (Wiley Series in Discrete Mathematics and Optimization)
April 26, 2019
A lively invitation to the flavor, elegance, and power of graphtheory
This mathematically rigorous introduction is tempered and enlivenedby numerous illustrations, revealing examples, seductiveapplications, and historical references. An award-winning teacher,Russ Merris has crafted a book designed to attract and engagethrough its spirited exposition, a rich assortment of well-chosenexercises, and a selection of topics that emphasizes the kinds ofthings that can be manipulated, counted, and pictured. Intendedneither to be a comprehensive overview nor an encyclopedicreference, this focused treatment goes deeply enough into asufficiently wide variety of topics to illustrate the flavor,elegance, and power of graph theory.
Another unique feature of the book is its user-friendly modularformat. Following a basic foundation in Chapters 1-3, the remainderof the book is organized into four strands that can be exploredindependently of each other. These strands center, respectively,around matching theory; planar graphs and hamiltonian cycles;topics involving chordal graphs and oriented graphs that naturallyemerge from recent developments in the theory of graphic sequences;and an edge coloring strand that embraces both Ramsey theory and aself-contained introduction to Pólya’s enumeration ofnonisomorphic graphs. In the edge coloring strand, the reader ispresumed to be familiar with the disjoint cycle factorization of apermutation. Otherwise, all prerequisites for the book can be foundin a standard sophomore course in linear algebra.
The independence of strands also makes Graph Theory an excellentresource for mathematicians who require access to specific topicswithout wanting to read an entire book on the subject.