Given this is the second edition of a respected text, it is important to examine what has changed and how the text has improved. Using an “algorithmic viewpoint,” the authors explore the standard aspects of graph theory—complements, paths, walks, subgraphs, trees, cycles, connectivity, symmetry, network flows, digraphs, colorings, graph matchings, and planar graphs. The expanded topics include explorations of subgraph counting, graphs and symmetries via permutation groups, graph embeddings on topological surfaces such as the Klein bottle and the double torus, and the connections of graphs to linear programming, including the primal-dual algorithm and discrete considerations, where the integral variables are bounded. Other text changes include some proof corrections and meaningful content revisions. Each chapter section contains rich exercise sets, complemented by chapter notes and an extensive bibliography. The authors’ claim is correct—their style is "rigorous, but informal," insightful, and it works. The text’s algorithms are generic in style, and usable with any major language. In summary, aimed at computer science and mathematics students, this revised text on graph theory will both challenge upper-level undergraduates and provide a comprehensive foundation for graduate students.--J. Johnson, Western Washington University
