On Subfamilies of AT-Free Graphs

Authors:
Ekkehard Köhler;Derek G. Corneil;Stephan Olariu;Lorna Stewart
Affiliations:
-;-;-;-
Venue:
WG '01 Proceedings of the 27th International Workshop on Graph-Theoretic Concepts in Computer Science
Year:
2001

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Abstract

We introduce two subfamilies of AT-free graphs, namely, path orderable graphs and strong asteroid free graphs. Path orderable graphs are defined by a linear ordering of the vertices that is a natural generalization of the ordering that characterizes cocomparability graphs. On the other hand, motivation for the definition of strong asteroid free graphs comes from the fundamental work of Gallai on comparability graphs. We show that cocomparability graphs 驴 path orderable graphs 驴 strong asteroid free graphs 驴 AT-free graphs. In addition, we settle the recognition question for the two new classes by proving that recognizing path orderable graphs is NP-complete whereas the recognition problem for strong asteroid free graphs can be solved in polynomial time.