Frugal, acyclic and star colourings of graphs Original Research Article

Given a graph image, a vertex colouring of image is image-frugal if no colour appears more than image times in any neighbourhood and is acyclic if each of the bipartite graphs consisting of the edges between any two colour classes is acyclic. For graphs of bounded maximum degree, Hind et al. (1997) studied proper image-frugal colourings and Yuster (1998) studied acyclic proper 2-frugal colourings. In this paper, we expand and generalise this study.