An arc of a graph is an oriented edge and a 3-arc is a 4-tuple (v, u, x, y) of vertices such that both (v, u, x) and (u, x, y) are paths of length two. The 3-arc graph of a graph ...
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...
The Lov´asz theta number of a graph G can be viewed as a semidefinite programming relaxation of the stability number of G. It has recently been shown that a copositive strengthe...
Hadwiger’s conjecture states that every graph with chromatic number χ has a clique minor of size χ. In this paper we prove a weakened version of this conjecture for the class ...
Suppose G is a graph. The chromatic Ramsey number rc(G) of G is the least integer m such that there exists a graph F of chromatic number m for which the following is true: For any...
A simple characterization of the 3, 4, or 5-colorable Eulerian triangulations of the projective plane is given. Key words: Projective plane, triangulation, coloring, Eulerian grap...
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...
Erdos proved that there are graphs with arbitrarily large girth and chromatic number. We study the extension of this for generalized chromatic numbers. Generalized graph coloring d...
The concept of circular chromatic number of graphs was introduced by Vince(1988). In this paper we define circular chromatic number of uniform hypergraphs and study their basic pr...