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Backbone colorings for graphs

By H.J. Broersma, F.V. Fomin, P.A. Golovach, G.J. Woeginger and H.L. Bodlaender

Abstract

We study backbone colorings, a variation on classical vertex colorings: Given a graph G=(V,E) and a spanning subgraph H (the backbone) of G, a backbone coloring for G and H is a proper vertex coloring V ¿{ 1,2,... } in which the colors assigned to adjacent vertices in H differ by at least two. We concentrate on the cases where the backbone is either a spanning tree or a spanning path. For tree backbones of G, the number of colors needed for a backbone coloring of G can roughly differ by a multiplicative factor of at most 2 from the chromatic number ¿(G); for path backbones this factor is roughly 3 2 . In the special case of split graphs G, the difference from ¿(G) is at most an additive constant 2 or 1, for tree backbones and path backbones, respectively. The computational complexity of the problem ‘Given a graph G, a spanning tree T of G, and an integer l, is there a backbone coloring for G and T with at most l colors?’ jumps from polynomial to NP-complete between l¿=¿4 (easy for all spanning trees) and l¿=¿5 (difficult even for spanning paths)

Publisher: Springer
Year: 2003
DOI identifier: 10.1007/978-3-540-39890-5_12
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Provided by: NARCIS
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