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基本説明
Systematically treats the Cartesian, strong, direct, and lexicographic product of graphs and graphs isometrically embeddable into them.
Full Description
Handbook of Product Graphs, Second Edition examines the dichotomy between the structure of products and their subgraphs. It also features the design of efficient algorithms that recognize products and their subgraphs and explores the relationship between graph parameters of the product and factors. Extensively revised and expanded, the handbook presents full proofs of many important results as well as up-to-date research and conjectures.
Results and Algorithms New to the Second Edition:
Cancellation results
A quadratic recognition algorithm for partial cubes
Results on the strong isometric dimension
Computing the Wiener index via canonical isometric embedding
Connectivity results
A fractional version of Hedetniemi's conjecture
Results on the independence number of Cartesian powers of vertex-transitive graphs
Verification of Vizing's conjecture for chordal graphs
Results on minimum cycle bases
Numerous selected recent results, such as complete minors and nowhere-zero flows
The second edition of this classic handbook provides a thorough introduction to the subject and an extensive survey of the field. The first three parts of the book cover graph products in detail. The authors discuss algebraic properties, such as factorization and cancellation, and explore interesting and important classes of subgraphs. The fourth part presents algorithms for the recognition of products and related classes of graphs. The final two parts focus on graph invariants and infinite, directed, and product-like graphs. Sample implementations of selected algorithms and other information are available on the book's website, which can be reached via the authors' home pages.
Contents
A Brief Introduction to Graphs and Their Products. Factorization and Cancellation. Isometric Embeddings. Algorithms. Invariants. Related Concepts. Appendix. Bibliography. Indices.
