In order to perform an average-case analysis for specific input distributions one needs to derive and understand properties of a 'typical' input instance. In the case of...
For any graph G, the k-improper chromatic number k (G) is the smallest number of colours used in a colouring of G such that each colour class induces a subgraph of maximum degree ...
The main aim of this short paper is to answer the following question. Given a fixed graph H, for which values of the degree d does a random d-regular graph on n vertices contain ...
We present a simple heuristic for finding a small connected dominating set of cubic graphs. The average-case performance of this heuristic, which is a randomised greedy algorithm,...
How to color 3 colorable graphs with few colors is a problem of longstanding interest. The best polynomial-time algorithm uses n0.2072 colors. There are no indications that colori...