A new linear algorithm for the two path problem on chordal graphs
Let G= (V,E) be a finite undirected graph with four distinguished vertices s, t, u, v. The two path problem (TPP) is to determine whether there exist two vertex disjoint paths connecting s with t and u with v and to find such paths if they exist.
In this paper, a simple and efficient algorithm for TPP restricted to 2-connected chordal graphs is given. The reduction of TPP for a general chordal graph to the TPP for a 2-connected chordal graph is outlined.
KeywordsDisjoint Path Chordal Graph Block Graph Vertex Disjoint Path Biconnected Component
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- 1.Ebert,J., A Linear Disjoint Path Algorithm, Proceedings WG82, Munich: Hanser Verlag (1982) 37–45.Google Scholar
- 2.Golumbic,M.C., Algorithmic Graph Theory and Perfect Graphs, Academic Press 1980.Google Scholar
- 3.Ohtsuki, T., The two disjoint path problem and wire routing design, Graph Theory and Algorithms (Eds. Saito,N. and Nishizeki,T.) Springer 108 (1980) 207–216.Google Scholar
- 4.Perl, Y. and Shiloach, Y., Finding two disjoint paths between two pairs of vertices in a graph, Journal of ACM, 25 (1978) 1–9.Google Scholar
- 5.Ramprasad,P.B. and Pandu Rangan,C., A new linear algorithm for the two path problem on planar graphs (To appear).Google Scholar
- 6.Shiloach, Y., A polynomial solution to the undirected two path problem, Journal of ACM, 27 (1980) 445–456.Google Scholar