On minimizing the number of label transitions around a vertex of a planar graph

Authors:
Bojan Mohar;Petr Škoda
Affiliations:
Department of Mathematics, Simon Fraser University, Burnaby, BC, Canada;Department of Mathematics, Simon Fraser University, Burnaby, BC, Canada
Venue:
IWOCA'11 Proceedings of the 22nd international conference on Combinatorial Algorithms
Year:
2011

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Abstract

We study the minimum number of label transitions around a given vertex v0 in a planar multigraph G in which the edges incident with v0 are labelled with integers 1, .…, l, where the minimum is taken over all embeddings of G in the plane. For a fixed number of labels, a linear-time FPT algorithm that (given the labels around v0) computes the minimum number of label transitions around v0 is presented. If the number of labels is unconstrained, then the problem of deciding whether the minimum number of label transitions is at most k is NP-complete.