Recognizing HH-free, HHD-free, and Welsh-Powell Opposition Graphs
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...
Main Authors: | , |
---|---|
Format: | Article |
Language: | English |
Published: |
Discrete Mathematics & Theoretical Computer Science
2006-01-01
|
Series: | Discrete Mathematics & Theoretical Computer Science |
Online Access: | http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/454 |
id |
doaj-4a4fb90d18954eb29694e3eac3200c9c |
---|---|
record_format |
Article |
spelling |
doaj-4a4fb90d18954eb29694e3eac3200c9c2020-11-25T00:59:11ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1462-72641365-80502006-01-0181Recognizing HH-free, HHD-free, and Welsh-Powell Opposition GraphsStavros D. NikolopoulosLeonidas PaliosIn 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 G 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. http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/454 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Stavros D. Nikolopoulos Leonidas Palios |
spellingShingle |
Stavros D. Nikolopoulos Leonidas Palios Recognizing HH-free, HHD-free, and Welsh-Powell Opposition Graphs Discrete Mathematics & Theoretical Computer Science |
author_facet |
Stavros D. Nikolopoulos Leonidas Palios |
author_sort |
Stavros D. Nikolopoulos |
title |
Recognizing HH-free, HHD-free, and Welsh-Powell Opposition Graphs |
title_short |
Recognizing HH-free, HHD-free, and Welsh-Powell Opposition Graphs |
title_full |
Recognizing HH-free, HHD-free, and Welsh-Powell Opposition Graphs |
title_fullStr |
Recognizing HH-free, HHD-free, and Welsh-Powell Opposition Graphs |
title_full_unstemmed |
Recognizing HH-free, HHD-free, and Welsh-Powell Opposition Graphs |
title_sort |
recognizing hh-free, hhd-free, and welsh-powell opposition graphs |
publisher |
Discrete Mathematics & Theoretical Computer Science |
series |
Discrete Mathematics & Theoretical Computer Science |
issn |
1462-7264 1365-8050 |
publishDate |
2006-01-01 |
description |
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 G 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. |
url |
http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/454 |
work_keys_str_mv |
AT stavrosdnikolopoulos recognizinghhfreehhdfreeandwelshpowelloppositiongraphs AT leonidaspalios recognizinghhfreehhdfreeandwelshpowelloppositiongraphs |
_version_ |
1725218541045547008 |