Critical and Anticritical Edges in Perfect Graphs

We call an edge e of a perfect graph G critical if G − e is imperfect and say further that e is anticritical with respect to the complementary graph G. We ask in which perfect graphs critical and anticritical edges occur and how to find critical and anticritical edges in perfect graphs. Finally, we study whether we can order the edges of certain perfect graphs such that deleting all the edges yields a sequence of perfect graphs ending up with a stable set.

• Type: Conference
• Year: 2001
• Where: WG
• Authors: Annegret Wagler
• Keywords: Anticritical Edges, Complementary Graph G, Perfect Graphs, Theoretical Computer Science, WG 2001