We describe a set of necessary conditions for a given graph to be the visibility graph of a simple polygon. For every graph satisfying these conditions we show that a uniform rank ...
In the strong edge coloring problem, the objective is to color the edges of the given graph with the minimum number of colors so that every color class is an induced matching. In ...
Hyperplanes of the form xj = xi + c are called affinographic. For an affinographic hyperplane arrangement in Rn, such as the Shi arrangement, we study the function f(m) that counts...
We provide a certifying algorithm for the problem of deciding whether a P5-free graph is 3-colorable by showing there are exactly six finite graphs that are P5-free and not 3-colo...
We show that every plane graph with maximum face size four whose all faces of size four are vertex-disjoint is cyclically 5-colorable. This answers a question of Albertson whether...