On a heterochromatic number for hypercubes

Abstract

The neighbourhood heterochromatic number nhc(G) of a non-empty graphG is the smallest integer l such that for every colouring of G with exactly l colours, G contains a vertex all of whose neighbours have different colours. We prove that limn→∞(nhc(Gn)− 1)/|V (Gn)| = 1 for any connected graph G with at least two vertices. We also give upper and lower bounds for the neighbourhood heterochromatic number of the 2n-dimensional hypercube. © 2007 Elsevier B.V. All rights reserved.

DOI: 10.1016/j.disc.2007.07.003

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Cite this paper

@article{MontellanoBallesteros2008OnAH, title={On a heterochromatic number for hypercubes}, author={Juan Jos{\'e} Montellano-Ballesteros and Victor Neumann-Lara and Eduardo Rivera-Campo}, journal={Discrete Mathematics}, year={2008}, volume={308}, pages={3441-3448} }