# DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

# IMPACT FACTOR 2018: 0.741

SCImago Journal Rank (SJR) 2018: 0.763

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# Discussiones Mathematicae Graph Theory

## EDGE-DISJOINT PATHS IN PERMUTATION GRAPHS

C. P. Gopalakrishnan
and
C. Pandu Rangan

Department of Computer Science, Indian Institute of Technology
Madras 600 036, India
e-mail: rangan@iitm.ernet.in

## Abstract

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

Keywords: algorithm, bridge, connectivity, disjoint paths, permutation graph.

1991 Mathematics Subject Classification: 058C85, 05C38

## References

 [AKP] K. Arvind, V. Kamakoti, C. Pandu Rangan, Efficient Parallel Algorithms for Permutation Graphs, to appear in Journal of Parallel and Distributed Computing. [BM 80] J. A. Bondy, U.S.R. Murty, Graph Theory with Applications, (Macmillan Press, 1976). [C 80] A. Cypher, An approach to the   k   paths problem, Proc. of the 12th STOC (1980) 211-217. [G 80] M. C. Golumbic, Algorithmic Graph Theory and Perfect Graphs, (Academic Press, 1980). [F 85] A. Frank, Edge-disjoint paths in planar graphs, J. Combin. Theory (B) 39 (1985) 164-178, doi: 10.1016/0095-8956(85)90046-2. [GP] C. P. Gopalakrishnan, C. Pandu Rangan, The two paths problem on permutation graphs, (submitted). [LR 78] A. LaPaugh, R. L. Rievest, The subgraph homeomorphism problem, Proc. of the 10th STOC (1978) 40-50. [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 graph, J. of the ACM 25 (1978) 1-9, doi: 10.1145/322047.322048. [RP] P. B. Ramprasad, C. Pandu Rangan, A new linear time algorithm for the two path problem on planar graphs, to appear. [S 90] A. Schwill, Nonblocking graphs: Greedy algorithms to compute disjoint paths, Proc. of the 7th STACS (1990) 250-262. [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. [S 83] J. Spinrad, Transitive orientation in   O(n2)   time, Proc. of Fifteenth ACM Symposium on the Theory of Computing (1983) 457-466, doi: 10.1145/800061.808777. [SP 91] A. Srinivasa Rao, C. Pandu Rangan, Linear algorithms for parity path and two path problems on circular arc graphs, BIT 31 (1991) 182-193. [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.