| author: | Stavros D. Nikolopoulos and Leonidas Palios |
|---|---|
| title: | Recognizing HH-free, HHD-free, and Welsh-Powell Opposition Graphs |
| keywords: | HH-free graph, HHD-free graph, Welsh-Powell opposition graph, perfectly orderable graph, recognition. |
| abstract: | 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 log 2 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 log 2 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 G G is HH-free can be efficiently resolved in O(n m) time using O(n space, which leads to an 2 )O(n m) -time and O(n -space algorithm for recognizing WPO-graphs. The previously best algorithms for recognizing HH-free, HHD-free, and WPO-graphs required 2 )O(n time and 3 )O(n space.2 ) |
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| reference: | Stavros D. Nikolopoulos and Leonidas Palios (2006), Recognizing HH-free, HHD-free, and Welsh-Powell Opposition Graphs, Discrete Mathematics and Theoretical Computer Science 8, pp. 65-82 |
| bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |
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