Recognition and Orientation Algorithms for P4-Comparability Graphs

  • Stavros D. Nikolopoulos
  • Leonidas Palios
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2223)


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 Hoáng 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 given graph. Recently, Raschle and Simon described O(n + m 2)-time algorithms for these problems, where m is the number of edges of the graph. In this paper, we describe difierent O(n + m 2)-time algorithms for the recognition and the acyclic P 4-transitive orientation problems on P 4- comparability graphs. Instrumental in these algorithms are structural relationships of the P 4-components of a graph, which we establish and which are interesting in their own right. Our algorithms are simple, use simple data structures, and have the advantage over those of Raschle and Simon in that they are non-recursive, require linear space and admit effcient parallelization.


Time Algorithm Directed Cycle Permutation Graph Topological Sorting Simple Undirected Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Stavros D. Nikolopoulos
    • 1
  • Leonidas Palios
    • 1
  1. 1.Department of Computer ScienceUniversity of IoanninaIoanninaGreece

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