Recognizing HHD-free and Welsh-Powell Opposition Graphs

Recognizing HH-free, HHD-free, and Welsh-Powell Opposition Graphs

In this paper, we consider the recognition problem on three classes of perfect graphs, namely, the HH-free, the HHDfree, and the Welsh-Powell opposition graphs (or WPO-graphs). In particular, we prove properties of the chordal completion of a graph and show that a modified version of the classic linear-time algorithm for testing for a perfect elimination ordering can be efficiently used to dete...

Re ognizing HHD - free and Welsh - PowellOpposition Graphs ?

An O ( nm )-Time Certifying Algorithm for Recognizing HHD-Free Graphs

In this paper, we consider the recognition problem on a class of perfectly orderable graphs, namely, the HHD-free graphs; such graphs do not contain any induced subgraph isomorphic to a house, a hole, or a domino. We prove properties of the HHD-free graphs which enable us to present an O(n m)-time and O(n + m)-space algorithm for determining whether a graph on n vertices and m edges is HHD-free...

Duchet-type theorems for powers of HHD-free graphs

Using the idea due to P. DUCHET in proving his well–known theorem on powers of chordal graphs, we shall describe some theorems of DUCHET–type for powers of graphs that have no long induced cycles. In particular, our DUCHET–type theorem for HHD–free graphs improves a recent result due to DRAGAN, NICOLAI, BRANDSTÄDT saying that odd powers of HHD–free graphs are also HHD–free.

Convexity and HHD-Free Graphs

It is well known that chordal graphs can be characterized via m-convexity. In this paper we introduce the notion of m-convexity (a relaxation of m-convexity) which is closely related to semisimplicial orderings of graphs. We present new characterizations of HHD-free graphs via m -convexity and obtain some results known from [B. Jamison and S. Olariu, Adv. Appl. Math., 9 (1988), pp. 364–376] as ...