T. Nishizeki Livres

This book features most of the important theorems and algorithms related to planar graphs. Eminently suitable as a text, it also is useful for researchers and includes an extensive reference section.The authors, who have researched planar graphs for many years, have structured the topics in a manner relevant to graph theorists and computer scientists. The first two chapters are introductory and provide the foundations of the graph theoretic notions and algorithmic techniques used throughout the text. Succeeding chapters discuss planarity testing and embedding, drawing planar graphs, vertex- and edge-coloring, independent vertex sets, and subgraph listing. The text concludes with explorations of planar separator theorem, Hamiltonian cycles, and single-commodity or multi-commodity flows.

Dividing a system into almost unidirectional blocks.- A linear algorithm for five-coloring a planar graph.- On the layering problem of multilayer PWB wiring.- A status on the linear arboricity.- On centrality functions of a graph.- Canonical decompositions of symmetric submodular systems.- The subgraph homeomorphism problem on reducible flow graphs.- Combinatorial problems on series-parallel graphs.- A graph-planarization algorithm and its application to random graphs.- Some common properties for regularizable graphs, edge-critical graphs and b-graphs.- "Dualities" in graph theory and in the related fields viewed from the metatheoretical standpoint.- On central trees of a graph.- On polynomial time computable problems.- Homomorphisms of graphs and their global maps.- Algorithms for some intersection graphs.- An efficient algorithm to find a Hamiltonian circuit in a 4-connected maximal planar graph.- Characterization of polyhex graphs as applied to chemistry.- The two disjoint path problem and wire routing design.