A Survey of the Algorithmic Properties of Simplicial, Upper Bound and Middle Graphs

Abstract

Three classes of graphs, simplicial, upper bound, and middle graphs, have been known for some time, but many of their algorithmic properties have not been published. The definitions for these graph classes are reviewed, and their relationships with other common graph classes (especially line and perfect graphs) are presented. Efficient algorithms are referenced or outlined to recognize each class of graphs. Finally, for each class of graphs and most of the common parameters of graphs, either an algorithm or an NP-complete result is presented, or it is referenced in the literature.