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Λ-backbone colorings along pairwise disjoint stars and matchings.

Broersma, H. J. and Fujisawa, J. and Marchal, L. and Paulusma, Daniel and Salman, A. N. M. and Yoshimoto, K. (2009) 'Λ-backbone colorings along pairwise disjoint stars and matchings.', Discrete mathematics., 309 (18). pp. 5596-5609.

Abstract

Given an integer λ≥2, a graph G=(V,E) and a spanning subgraph H of G (the backbone of G), a λ-backbone coloring of (G,H) is a proper vertex coloring V→{1,2,…} of G, in which the colors assigned to adjacent vertices in H differ by at least λ. We study the case where the backbone is either a collection of pairwise disjoint stars or a matching. We show that for a star backbone S of G the minimum number ℓ for which a λ-backbone coloring of (G,S) with colors in {1,…,ℓ} exists can roughly differ by a multiplicative factor of at most 2- 1/Λ from the chromatic number χ(G). For the special case of matching backbones this factor is roughly 2- 2/(Λ+1). We also show that the computational complexity of the problem “Given a graph G with a star backbone S, and an integer ℓ, is there a λ-backbone coloring of (G,S) with colors in {1,…,ℓ}?” jumps from polynomially solvable to NP-complete between ℓ=λ+1 and ℓ=λ+2 (the case ℓ=λ+2 is even NP-complete for matchings). We finish the paper by discussing some open problems regarding planar graphs.

Item Type:Article
Keywords:λ-backbone coloring, λ-backbone coloring number, Star, Matching.
Full text:Full text not available from this repository.
Publisher Web site:http://dx.doi.org/10.1016/j.disc.2008.04.007
Record Created:15 Dec 2009 11:35
Last Modified:03 Apr 2013 13:12

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