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Journal Articles Discrete Mathematics Year : 2010

Acyclic improper colourings of graphs with bounded maximum degree

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].

Dates and versions

lirmm-00433038 , version 1 (18-11-2009)

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Cite

Louigi Addario-Berry, Louis Esperet, Ross Kang, Colin Mcdiarmid, Alexandre Pinlou. Acyclic improper colourings of graphs with bounded maximum degree. Discrete Mathematics, 2010, 310 (2), pp.223-229. ⟨10.1016/j.disc.2008.09.009⟩. ⟨lirmm-00433038⟩
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