Recognizing HHD-free and Welsh-Powell opposition graphs
(EN)
Nikolopoulos, S. D.
(EN)
Πανεπιστήμιο Ιωαννίνων. Σχολή Θετικών Επιστημών. Τμήμα Μηχανικών Ηλεκτρονικών Υπολογιστών και Πληροφορικής
(EL)
Nikolopoulos, S. D.
(EN)
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 " modified version of the classic linear-time algorithm for testing for " perfect elimination ordering can be efficiently used to determine in O(min{nmalpha(n), nm + n(2) 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{nmalpha(n), nm+n(2) log n})-time and O(n+m)-space algorithm for recognizing HHD-free graphs. We also show that determining whether the complement (G) over bar of the graph G contains a house or a hole can be efficiently resolved in O(nm) time using O(n(2)) space, this in turn leads to an O(nm)-time and O(n(2))-space algorithm for recognizing WPO-graphs. The previously best algorithms for recognizing HHD-free and WPO-graphs required O(n(3)) time and O(n(2)) space.
(EN)
