On Minimizing the Number of Label Transitions around a Vertex of a Planar Graph
We study the minimum number of label transitions around a given vertex v 0 in a planar multigraph G in which the edges incident with v 0 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 v 0) computes the minimum number of label transitions around v 0 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.
Keywordslabel transitions planar graph fixed-parameter tractable
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