Topics in intersection graph theory - MacKee, Terry A.; McMorris, Fred R. (Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 1999)
Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader
Includes bibliographical references (p. 149-200) and index
Preface -- 1. Intersection graphs -- Basic concepts -- Intersection classes -- Parsimonious set representations -- Clique graphs -- Line graphs -- Hypergraphs -- 2. Chordal graphs -- Chordal graphs as intersection graphs -- Other characterizations -- Tree hypergraphs -- Some applications of chordal graphs -- Split graphs -- 3. Interval graphs -- Definitions and characterizations -- Interval hypergraphs -- Proper interval graphs -- Some applications of interval graphs -- 4. Competition graphs -- Neighborhood graphs -- Competition graphs -- Interval competition graphs -- Upper bound graphs -- 5. Threshold graphs -- Definitions and characterizations -- Threshold graphs as intersection graphs -- Difference graphs and Ferrers digraphs -- Some applications of threshold graphs -- 6. Other kinds of intersection -- p-Intersection graphs -- Intersection multigraphs and pseudographs -- Tolerance intersection graphs -- 7. Guide to related topics -- Assorted geometric intersection graphs -- Bipartite intersection graphs, intersection digraphs, and catch (di)graphs -- Chordal bipartite and weakly chordal graphs -- Circle graphs and permutation graphs -- Clique graphs of chordal graphs and clique-helly graphs -- Containment, comparability, cocomparability, and asteroidal triple-free graphs -- Infinite intersection graphs -- Miscellaneous topics -- P4-free chordal graphs and cographs -- Powers of intersection graphs -- Sphere-of-influence graphs -- Strongly chordal graphs -- Bibliography -- Index
Finally there is a book that presents real applications of graph theory in a unified format. This book is the only source for an extended, concentrated focus on the theory and techniques common to various types of intersection graphs. It is a concise treatment of the aspects of intersection graphs that interconnect many standard concepts and form the foundation of a surprising array of applications to biology, computing, psychology, matrices, and statistics
Keywords: Intersection graph theory; Graphentheorie