Linear structure of bipartite permutation graphs and the longest path problem

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. Key words: Bipartite permutation graphs; Graph decomposition; Linear time algorithms.

• Type: Journal
• Year: 2007
• Where: IPL
• Authors: Ryuhei Uehara, Gabriel Valiente
• Keywords: Bipartite Permutation Graphs, Decomposition, IPL 2007, Permutation Graphs