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

Recognizing HHD-free and Welsh-Powell Opposition Graphs

In this paper, we consider the recognition problem on two classes of perfectly orderable graphs, namely, the HHD-free and the Welsh-Powell opposition graphs (or WPOgraphs). 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 determin...

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.

Algorithms for the Treewidth and Minimum Fill-in of HHD-Free Graphs

K e y w o r d s : graphs, algori thms, HHD-free graphs, t reewidth, min imum fill-in. MSC: 68R10. 1 I n t r o d u c t i o n A graph is HHD-free if it does not contain a house (i.e., the complement of Ps), a hole (Ck for k _> 5) or a domino (see Figure 1). Fig. 1. 'House' (left), 'hole' (middle) and 'domino' (right) * kloks@math, utwente, nl