Planarization and fragmentability of some classes of graphs

The coefficient of fragmentability of a class of graphs measures the proportion of vertices that need to be removed from the graphs in the class in order to leave behind bounded sized components. We have previously given bounds on this parameter for the class of graphs satisfying a given constant bound on maximum degree. In this paper, we give fragmentability bounds for some classes of graphs of bounded average degree, as well as classes of given thickness, the class of k-colourable graphs, and the class of n-dimensional cubes. In order to establish the fragmentability results for bounded average degree, we prove that the proportion of vertices that must be removed from a graph of average degree at most

• Type: Journal
• Year: 2008
• Where: DM
• Authors: Keith Edwards, Graham Farr
• Keywords: Average Degree, Constant Bound, DM 2008, Planar Subgraph