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Acyclic improper colourings of graphs with bounded maximum degree

Louigi Addario-Berry 1 Louis Esperet 2 Ross Kang 1 Colin Mcdiarmid 1 Alexandre Pinlou 3
2 G-SCOP_OC - Optimisation Combinatoire
G-SCOP - Laboratoire des sciences pour la conception, l'optimisation et la production
3 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : For graphs of bounded maximum degree, we consider acyclic t-improper colourings, that is, colourings in which each bipartite subgraph consisting of the edges between two colour classes is acyclic, and each colour class induces a graph with maximum degree at most t. We consider the supremum, over all graphs of maximum degree at most d, of the acyclic t-improper chromatic number and provide t-improper analogues of results by Alon, McDiarmid and Reed [N. Alon, C.J.H. McDiarmid, B. Reed, Acyclic coloring of graphs, Random Structures Algorithms 2 (3) (1991) 277–288] and Fertin, Raspaud and Reed [G. Fertin, A. Raspaud, B. Reed, Star coloring of graphs, J. Graph Theory 47 (3) (2004) 163–182].
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Submitted on : Wednesday, November 18, 2009 - 7:12:35 AM
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Louigi Addario-Berry, Louis Esperet, Ross Kang, Colin Mcdiarmid, Alexandre Pinlou. Acyclic improper colourings of graphs with bounded maximum degree. Discrete Mathematics, Elsevier, 2010, 310 (2), pp.223-229. ⟨10.1016/j.disc.2008.09.009⟩. ⟨lirmm-00433038⟩



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