Linear structure of bipartite permutation graphs and the longest path problem

doi:10.1016/j.ipl.2007.02.010

Information Processing Letters

Volume 103, Issue 2, 16 July 2007, Pages 71-77

https://doi.org/10.1016/j.ipl.2007.02.010 Get rights and content

Abstract

The class of bipartite permutation graphs is the intersection of two well known graph classes: bipartite graphs and permutation graphs. A complete bipartite decomposition of a bipartite permutation graph is proposed in this note. The decomposition gives a linear structure of bipartite permutation graphs, and it can be obtained in $O (n)$ time, where n is the number of vertices. As an application of the decomposition, we show an $O (n)$ time and space algorithm for finding a longest path in a bipartite permutation graph.

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¹: Partially supported by Spanish CICYT project GRAMMARS (TIN 2004-07925-C03-01) and by the Japan Society for the Promotion of Science through Long-term Invitation Fellowship L05511 for visiting JAIST (Japan Advanced Institute of Science and Technology).

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Linear structure of bipartite permutation graphs and the longest path problem

Abstract

Information Processing Letters

Discrete Mathematics

Discrete Mathematics

Discrete Applied Mathematics

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