Graph Theory and Its Applications

Graph Theory and Its Applications, Third Editionis the latest edition of the international, bestselling textbook for undergraduate courses in graph theory, yet it is expansive enough to be used for graduate courses as well. The textbook takes a comprehensive, accessible approach to graph theory, integrating careful exposition of classical developments with emerging methods, models, and practical needs. The authors’ unparalleled treatment is an ideal text for a two-semester course and a variety of one-semester classes, from an introductory one-semester course to courses slanted toward classical graph theory, operations research, data structures and algorithms, or algebra and topology.Features of the Third EditionExpanded coverage on several topics (e.g., applications of graph coloring and tree-decompositions)Provides better coverage of algorithms and algebraic and topological graph theory than any other text Incorporates several levels of carefully designed exercises that promote student retention and develop and sharpen problem-solving skillsIncludes supplementary exercises to develop problem-solving skills, solutions and hints, and a detailed appendix, which reviews the textbook’s topicsAbout the AuthorsJonathan 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 is also a mathematics professor at Rollins College. His research interest in graph theory centers on the topological or algebraic side.

Introduction to Graph ModelsGraphs and Digraphs. Common Families of Graphs. Graph Modeling Applications. Walks and Distance. Paths, Cycles, and Trees. Vertex and Edge Attributes.Structure and RepresentationGraph Isomorphism. Automorphism and Symmetry. Subgraphs. Some Graph Operations. Tests for Non-Isomorphism. Matrix Representation. More Graph Operations.TreesCharacterizations and Properties of Trees. Rooted Trees, Ordered Trees, and Binary Trees. Binary-Tree Traversals. Binary-Search Trees. Huffman Trees and Optimal Prefix Codes. Priority Trees. Counting Labeled Trees. Counting Binary Trees. Spanning TreesTree Growing. Depth-First and Breadth-First Search. Minimum Spanning Trees and Shortest Paths. Applications of Depth-First Search. Cycles, Edge-Cuts, and Spanning Trees. Graphs and Vector Spaces. Matroids and the Greedy Algorithm.ConnectivityVertex and Edge-Connectivity. Constructing Reliable Networks. Max-Min Duality and Menger’s Theorems. Block Decompositions.Optimal Graph TraversalsEulerian Trails and Tours. DeBruijn Sequences and Postman Problems. Hamiltonian Paths and Cycles. Gray Codes and Traveling Salesman Problems.Planarity and Kuratowski’s TheoremPlanar Drawings and Some Basic Surfaces. Subdivision and Homeomorphism. Extending Planar Drawings. Kuratowski’s Theorem. Algebraic Tests for Planairty. Planarity Algorithm. Crossing Numbers and Thickness. Graph ColoringsVertex-Colorings. Map-Colorings. Edge-Colorings. Factorization.Special Digraph ModelsDirected Paths and Mutual Reachability. Digraphs as Models for Relations. Tournaments. Project Scheduling. Finding the Strong Components of a Digraph.Network Flows and ApplicationsFlows and Cuts in Networks. Solving the Maximum-Flow Problem. Flows and Connectivity. Matchings, Transversals, and Vertex Covers.Graph Colorings and SymmetryAutomorphisms of Simple Graphs. Equivalence Classes of Colorings.Appendix

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 is also a mathematics professor at Rollins College. His research interest in graph theory centers on the topological or algebraic side.