### Volume 7

n° 1 (2005), pp. 231-254author: | Stavros D. Nikolopoulos and Leonidas Palios |
---|---|

title: | On the Recognition of Bipolarizable and P -simplicial Graphs4 |

keywords: | Bipolarizable (Raspail) graph, P -simplicial graph, perfectly orderable graph, recognition, algorithm, complexity4 |

abstract: | The classes of Raspail (also known as Bipolarizable) and P -simplicial graphs were introduced by Hoàng and Reed who showed that both classes are perfectly
orderable and admit polynomial-time recognition algorithms
HR1. In this paper, we consider the recognition problem on
these classes of graphs and present algorithms that solve it in
4 O(n m) time. In particular, we prove properties and show that we
can produce bipolarizable and P -simplicial orderings on the
vertices of the input graph 4 G , if such orderings exist, working
only on P s that participate in a 3 P of 4 G . The proposed
recognition algorithms are simple, use simple data structures and
both require O(n + m) space. Additionally, we show how our
recognition algorithms can be augmented to provide certificates,
whenever they decide that G is not bipolarizable or P -simplicial;
the augmentation takes 4 O(n + m) time and space.
Finally, we include a diagram on class inclusions and the
currently best recognition time complexities for a number of
perfectly orderable classes of graphs. |

If your browser does not display the abstract correctly (because of the different mathematical symbols) you may look it up in the PostScript or PDF files. | |

reference: | Stavros D. Nikolopoulos and Leonidas Palios (2005),
On the Recognition of Bipolarizable and P -simplicial Graphs,
4 Discrete Mathematics and Theoretical Computer Science 7, pp. 231-254 |

bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |

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Automatically produced on Tue Nov 8 22:14:23 CET 2005 by falk