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 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 determine in O(min{nmα(n), nm + n2 log n}) time whether a given graph G on n vertices and m edges contains a house or a hole; this leads to an O(min{nmα(n), nm+n2 log n})-time and O(n+m)-space algorithm for recognizing HHD-free graphs. We also show that determining whether the complement G of the graph G contains a house or a hole can be efficiently resolved in O(nm) time using O(n2 ) space; this in turn leads to an O(nm)-time and O(n2 )-space algorithm for recognizing WPOgraphs. The previously best algorithms for recognizing HHD-free and WPO-graphs required O(n3 ) time and O(n2 ) space.

• Type: Conference
• Year: 2004
• Where: WG
• Authors: Stavros D. Nikolopoulos, Leonidas Palios
• Keywords: Classic Linear-time Algorithm, Computer Science, Orderable Graphs, Welsh-Powell Opposition Graphs, WG 2004