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 ...
A graph G with n vertices and maximum degree G cannot be given weak sense of direction using less than G colours. It is known that n colours are always sufficient, and it was conje...
We present randomized approximation algorithms for the circular arc graph colouring problem and for the problem of bandwidth allocation in all-optical ring networks. We obtain a fa...
We study the empire colouring problem (as defined by Percy Heawood in 1890) for maps whose dual planar graph is a tree, with empires formed by exactly r countries. We prove that, ...
We present k-Flipper, a graph transformation algorithm that transforms regular undirected graphs. Given a path of k +2 edges it interchanges the end vertices of the path. By defin...