Treelike Comparability Graphs: Characterization, Recognition, and Applications

An undirected graph is a treelike comparability graph if it admits a transitive orientation such that its transitive reduction is a tree. We show that treelike comparability graphs are distance hereditary. Utilizing this property, we give a linear time recognition algorithm. We then characterize permutation graphs that are treelike. Finally, we consider the Partitioning into Bounded Cliques problem on special subgraphs of treelike permutation graphs.

• Type: Conference
• Year: 2004
• Where: WG
• Authors: Sabine Cornelsen, Gabriele Di Stefano
• Keywords: Computer Science, Permutation Graphs, Treelike Comparability Graphs, Treelike Permutation Graphs, WG 2004