(Circular) backbone colouring: tree backbones in planar graphs

Abstract : Consider an undirected graph G and a subgraph H of G, on the same vertex set. The q-backbone chromatic number BBCq(G,H) is the minimum k such that G can be properly coloured with colours from {1, ..., k}, and moreover for each edge of H, the colours of its ends differ by at least q. In this paper we focus on the case when G is planar and H is a forest. We give a series of NP-hardness results as well as upper bounds for BBCq(G,H), depending on the type of the forest (matching, galaxy, spanning tree). Eventually, we discuss a circular version of the problem.
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Submitted on : Thursday, November 29, 2012 - 7:01:43 PM
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Frédéric Havet, Andrew King, Mathieu Liedloff, Ioan Todinca. (Circular) backbone colouring: tree backbones in planar graphs. [Research Report] RR-8152, INRIA. 2012. ⟨hal-00759044⟩

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