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Finding a Longest Alternating Cycle in a 2-edge-coloured Complete Graph is in RP

Published online by Cambridge University Press:  12 September 2008

Rachid Saad
Rachid Saad
Affiliation:
Cité Ibn Khaldun, Bât 68 A2, Boumerdes, Algeria
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Abstract

Jackson [10] gave a polynomial sufficient condition for a bipartite tournament to contain a cycle of a given length. The question arises as to whether deciding on the maximum length of a cycle in a bipartite tournament is polynomial. The problem was considered by Manoussakis [12] in the slightly more general setting of 2-edge coloured complete graphs: is it polynomial to find a longest alternating cycle in such coloured graphs? In this paper, strong evidence is given that such an algorithm exists. In fact, using a reduction to the well known exact matching problem, we prove that the problem is random polynomial.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 5 , Issue 3 , September 1996 , pp. 297 - 306
Copyright
Copyright © Cambridge University Press 1996

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