Nikolopoulos, Stavros D. and Palios, Leonidas - Recognizing HH-free, HHD-free, and Welsh-Powell Opposition Graphs

dmtcs:370 - Discrete Mathematics & Theoretical Computer Science, January 1, 2006, Vol. 8
Recognizing HH-free, HHD-free, and Welsh-Powell Opposition Graphs

Authors: Nikolopoulos, Stavros D. and Palios, Leonidas

In this paper, we consider the recognition problem on three classes of perfectly orderable graphs, namely, the HH-free, 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(n min \m α (n,n), m + n^2 log n\) time whether a given graph G on n vertices and m edges contains a house or a hole; this implies an O(n min \m α (n,n), m + n^2 log n\)-time and O(n+m)-space algorithm for recognizing HH-free graphs, and in turn leads to an HHD-free graph recognition algorithm exhibiting the same time and space complexity. We also show that determining whether the complement øverlineG of the graph G is HH-free can be efficiently resolved in O(n m) time using O(n^2) space, which leads to an O(n m)-time and O(n^2)-space algorithm for recognizing WPO-graphs. The previously best algorithms for recognizing HH-free, HHD-free, and WPO-graphs required O(n^3) time and O(n^2) space.


Source : oai:HAL:hal-00961102v1
Volume: Vol. 8
Published on: January 1, 2006
Submitted on: March 26, 2015
Keywords: recognition.,perfectly orderable graph,recognition,HH-free graph,HHD-free graph,Welsh-Powell opposition graph,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]


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