# A linear algorithm for the two paths problem on permutation graphs

C.P. Gopalakrishnan; C. Pandu Rangan

Discussiones Mathematicae Graph Theory (1995)

- Volume: 15, Issue: 2, page 147-166
- ISSN: 2083-5892

## Access Full Article

top## Abstract

top## How to cite

topC.P. Gopalakrishnan, and C. Pandu Rangan. "A linear algorithm for the two paths problem on permutation graphs." Discussiones Mathematicae Graph Theory 15.2 (1995): 147-166. <http://eudml.org/doc/270239>.

@article{C1995,

abstract = {The 'two paths problem' is stated as follows. Given an undirected graph G = (V,E) and vertices s₁,t₁;s₂,t₂, the problem is to determine whether or not G admits two vertex-disjoint paths P₁ and P₂ connecting s₁ with t₁ and s₂ with t₂ respectively. In this paper we give a linear (O(|V|+ |E|)) algorithm to solve the above problem on a permutation graph.},

author = {C.P. Gopalakrishnan, C. Pandu Rangan},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {algorithm; bridge; connectivity; disjoint paths; permutation graph; two paths problem},

language = {eng},

number = {2},

pages = {147-166},

title = {A linear algorithm for the two paths problem on permutation graphs},

url = {http://eudml.org/doc/270239},

volume = {15},

year = {1995},

}

TY - JOUR

AU - C.P. Gopalakrishnan

AU - C. Pandu Rangan

TI - A linear algorithm for the two paths problem on permutation graphs

JO - Discussiones Mathematicae Graph Theory

PY - 1995

VL - 15

IS - 2

SP - 147

EP - 166

AB - The 'two paths problem' is stated as follows. Given an undirected graph G = (V,E) and vertices s₁,t₁;s₂,t₂, the problem is to determine whether or not G admits two vertex-disjoint paths P₁ and P₂ connecting s₁ with t₁ and s₂ with t₂ respectively. In this paper we give a linear (O(|V|+ |E|)) algorithm to solve the above problem on a permutation graph.

LA - eng

KW - algorithm; bridge; connectivity; disjoint paths; permutation graph; two paths problem

UR - http://eudml.org/doc/270239

ER -

## References

top- [BM 76] J.A. Bondy, U.S.R. Murthy, Graph Theory with Applications (Academic Press, 1976).
- [ET 75] S. Even, R.E. Tarjan, Network flow and testing graph connectivity, SIAM J. Comput. 4 (1975) 507-518, doi: 10.1137/0204043. Zbl0328.90031
- [HT 74] J.E. Hopcroft, R.E. Tarjan, Efficient planarity testing, J. ACM 21 (1974) 549-568, doi: 10.1145/321850.321852. Zbl0307.68025
- [G 80] M.C. Golumbic, Algorithmic Graph Theory and Perfect Graphs (Academic Press, 1980).
- [MT 89] B. Mishra, R.E. Tarjan, A linear time algorithm for finding an ambitus (Technical Report 464, August 1989, New York University).
- [O 80] T. Ohtsuki, The two disjoint path problem and wire routing design, In: Proc. of the 17th Symp. of Res. Inst. of Electrical Comm. (1980) 257-267.
- [PS 78] Y. Perl, Y. Shiloach, Finding two disjoint paths between two pairs of vertices in a graph, J. of the ACM 25 (1978) 1-9, doi: 10.1145/322047.322048. Zbl0365.68026
- [RP] P.B. Ramprasad, C. Pandu Rangan, A new linear time algorithm for the two path problem on planar graphs (Technical Report, Department of Computer Science, IIT, Madras, 1991).
- [S 80] Y. Shiloach, A polynomial solution to the undirected two paths problem, J. of the ACM 27 (1980) 445-456, doi: 10.1145/322203.322207. Zbl0475.68042
- [S 83] J. Spinrad, Transitive orientation in O(n²) time, In: Proc. of Fifteenth ACM Symposium on the Theory of Computing (1983) 457-466, doi: 10.1145/800061.808777.
- [KPS 91] S.V. Krishnan, C. Pandu Rangan, S. Seshadri, A. Schwill, Two Disjoint Paths in Chordal graphs (Technical Report, 2/91, February 1991, University of Oldenburg, Germany).

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.