A k-track drawing is a crossing-free 3D straight-line drawing of a graph G on a set of k parallel lines called tracks. The minimum value of k for which G admits a k-track drawing ...
We propose a new exact algorithm for finding the chromatic number of a graph G. The algorithm attempts to determine the smallest possible induced subgraph G' of G which has t...
Given a graph G whose set of vertices is a Polish space X, the weak Borel chromatic number of G is the least size of a family of pairwise disjoint G-independent Borel sets that cov...
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, ...