Treelike Comparability Graphs: Characterization, Recognition, and Applications
نویسندگان
چکیده
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.
منابع مشابه
Treelike Comparability Graphs
A comparability graph is a simple graph which admits a transitive orientation on its edges. Each one of such orientations defines a poset on the vertex set, and also it is said that this graph is the comparability graph of the poset. A treelike poset is a poset whose covering graph is a tree. Comparability graphs of arborescence posets are known as trivially perfect graphs. These have been char...
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