The smallest n such that every colouring of the edges of Kn must contain a monochromatic star K1,s+1 or a properly edge-coloured Kt is denoted by f(s, t). Its existence is guarant...
We consider the Chromatic Sum Problem on bipartite graphs which appears to be much harder than the classical Chromatic Number Problem. We prove that the Chromatic Sum Problem is NP...
Michal Malafiejski, Krzysztof Giaro, Robert Jancze...
We derive a sufficient condition for a sparse graph G on n vertices to contain a copy of a tree T of maximum degree at most d on (1 − )n vertices, in terms of the expansion prop...
Abstract. We present algorithmic lower bounds on the size of the largest independent sets of vertices in a random d-regular graph. Our bounds hold with probability approaching one ...
The graph inference from a walk for a class C of undirected edge-colored graphs is, given a string x of colors, nding the smallest graph G in C that allows a traverse of all edge...