Recognizing Bipolarizable and P4-Simplicial Graphs

  • Stavros D. Nikolopoulos
  • Leonidas Palios
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2880)

Abstract

Hoàng and Reed defined the classes of Raspail (also known as Bipolarizable) and P 4-simplicial graphs, both of which are perfectly orderable, and proved that they admit polynomial-time recognition algorithms [16]. In this paper, we consider the recognition problem on these classes of graphs and present algorithms that solve it in O(nm) time, where n and m are the numbers of vertices and of edges of the input graph. In particular, we prove properties and show that we can produce bipolarizable and P 4-simplicial orderings on the vertices of a graph G, if such orderings exist, working only on P 3s that participate in P 4s of G. The proposed recognition algorithms are simple, use simple data structures and require O(n+m) space. Moreover, we present a diagram on class inclusions and the currently best recognition time complexities for a number of perfectly orderable classes of graphs and some preliminary results on forbidden subgraphs for the class of P 4-simplicial graphs.

Keywords

Bipolarizable (Raspail) graph P4-simplicial graph perfectly orderable graph recognition algorithm complexity forbidden subgraph 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

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

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