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 Hedetniemias conjecture Results on the independence number of Cartesian powers of vertex-transitive graphs Verification of Vizingas 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 bookas website, which can be reached via the authorsa home pages.Feder points out a dichotomy: either there exists a polynomial algorithm for solving the problem, or the problem is NP-complete. ... one can construct two retractive mappings such that the problem of finding a common fixed point is NP- complete. ... It is an extension of a theorem of Feder (1995) from one contraction to a finite number of contractions. ... in G, if f is a nonexpansive mapping on G i 2Gj, and xixj, yiyj, zizj are fixed points of f, then gi(xi , yi , zi)gj(xj , yj , zj) is a fixed point of f as well.
|Title||:||Handbook of Product Graphs, Second Edition|
|Author||:||Richard Hammack, Wilfried Imrich, Sandi Klavžar|
|Publisher||:||CRC Press - 2011-06-06|