Acyclic improper colourings of graphs with bounded maximum degree

Journal article

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]. © 2009.

Authors: Addario-Berry, L; Esperet, L; Kang, R; McDiarmid, C; Pinlou, A

• Journal: Discrete Mathematics
• Volume: 310
• Issue: 2
• Pages: 223-229
• Publication date: 2010-01-28
• DOI: 10.1016/j.disc.2008.09.009
• ISSN: 0012-365X
• Language: English
• Keywords: Bounded degree graphs; Improper colouring; Acyclic colouring; Star colouring