A1 Refereed original research article in a scientific journal
Locally identifying colourings for graphs with given maximum degree
Authors: Foucaud F, Honkala I, Laihonen T, Parreau A, Perarnau G
Publisher: ELSEVIER SCIENCE BV
Publication year: 2012
Journal: Discrete Mathematics
Journal name in source: DISCRETE MATHEMATICS
Journal acronym: DISCRETE MATH
Number in series: 10
Volume: 312
Issue: 10
First page : 1832
Last page: 1837
Number of pages: 6
ISSN: 0012-365X
DOI: https://doi.org/10.1016/j.disc.2012.01.034(external)
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/2227592(external)
A proper vertex-colouring of a graph G is said to be locally identifying if for any pair u, v of adjacent vertices with distinct closed neighbourhoods, the sets of colours in the closed neighbourhoods of u and v are different. We show that any graph G has a locally identifying colouring with 2 Delta(2) - 3 Delta + 3 colours, where Delta is the maximum degree of G, answering in a positive way a question asked by Esperet et al. We also provide similar results for locally identifying colourings which have the property that the colours in the neighbourhood of each vertex are all different and apply our method to the class of chordal graphs. (c) 2012 Elsevier B.V. All rights reserved.
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