We prove that any finite set of half-planes can be colored by two colors so that every point of the plane, which belongs to at least three half-planes in the set, is covered by ha...
It is proved that there is a function f : N N such that the following holds. Let G be a graph embedded in a surface of Euler genus g with all faces of even size and with edge-wid...
Some results relating to the road-coloring conjecture of Alder, Goodwyn, and Weiss, which give rise to an O(n2) algorithm to determine whether or not a given edge-coloring of a gra...
E. Gocka, Walter W. Kirchherr, Edward F. Schmeiche...
The problem of computing the chromatic number of a P5-free graph (a graph which contains no path on 5 vertices as an induced subgraph) is known to be NP-hard. However, we show tha...
A linear equation L is called k-regular if every k-coloring of the positive integers contains a monochromatic solution to L. Richard Rado conjectured that for every positive intege...