Topics in Intersection Graph Theory

Preface Chapter 1: Intersection Graphs. Basic Concepts Intersection Classes Parsimonious Set Representations Clique Graphs Line Graphs Hypergraphs Chapter 2: Chordal Graphs. Chordal Graphs as Intersection Graphs Other Characterizations Tree Hypergraphs Some Applications of Chordal Graphs Split Graphs Chapter 3: Interval Graphs. Definitions and Characterizations Interval Hypergraphs Proper Interval Graphs Some Applications of Interval Graphs Chapter 4: Competition Graphs. Neighborhood Graphs Competition Graphs Interval Competition Graphs Upper Bound Graphs Chapter 5: Threshold Graphs. Definitions and Characterizations Threshold Graphs as Intersection Graphs Difference Graphs and Ferrers Digraphs Some Applications of Threshold Graphs Chapter 6: Other Kinds of Intersection. p-Intersection Graphs Intersection Multigraphs and Pseudographs Tolerance Intersection Graphs Chapter 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.