Finding an induced path of given parity in planar graphs in polynomial time

Authors:
Marcin Kamiński;Naomi Nishimura
Affiliations:
Université Libre de Bruxelles Belgium;University of Waterloo, Canada
Venue:
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Year:
2012

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Abstract

The problem of deciding, given a graph G and two vertices s and t, whether there exists an induced path of given parity between s and t in G is known to be NP-complete. We show how to solve the problem in O(|V (G)|7) time, when the input graph is planar. We use techniques from the theory of graph minors as well as the theory of perfect graphs.