Algorithms for P-4-comparability graph recognition and acyclic P-4-transitive orientation
(EN)
Nikolopoulos, S. D.
(EN)
Πανεπιστήμιο Ιωαννίνων. Σχολή Θετικών Επιστημών. Τμήμα Μηχανικών Ηλεκτρονικών Υπολογιστών και Πληροφορικής
(EL)
Nikolopoulos, S. D.
(EN)
We consider two problems pertaining to P-4-comparability graphs, namely, the problem of recognizing whether a simple undirected graph is a P-4-comparability graph and the problem of producing an acyclic P-4-transitive orientation of a P-4-comparability graph. These problems have been considered by HoAng and Reed who described o(n(4))- and o(n(5))-time algorithms for their solution, respectively, where n is the number of vertices of the input graph. Faster algorithms have recently been presented by Raschle and Simon, and by Nikolopoulos and Palios; the time complexity of these algorithms for either problem is o (n + m(2)), where m is the number of edges of the graph. In this paper we describe O (nm)-time and O (n + m)-space algorithms for the recognition and the acyclic P-4-transitive orientation problems on P-4-comparability graphs. The algorithms rely on properties of the P-4-components of a graph, which we establish, and on the efficient construction of the P4-components by means of the BFS-trees of the complement of the graph rooted at each of its vertices, without however explicitly computing the complement. Both algorithms are simple and use simple data structures.
(EN)
