The domatic number of a graph G is the maximum number of dominating sets into which the vertex set of G can be partitioned. We show that the domatic number of a random r-regular g...
An acyclic coloring of a graph G is a proper coloring of the vertex set of G such that G contains no bichromatic cycles. The acyclic chromatic number of a graph G is the minimum nu...
Let F1, F2, . . . , Fk be graphs with the same vertex set V . A subset S V is a factor dominating set if in every Fi every vertex not in S is adjacent to a vertex in S, and a fac...
Peter Dankelmann, Michael A. Henning, Wayne Goddar...
We study properties of the sets of minimal forbidden minors for the families of graphs having a vertex cover of size at most k. We denote this set by O(k-VERTEX COVER) and call it...
The packing chromatic number χρ(G) of a graph G is the smallest integer k such that the vertex set of G can be partitioned into packings with pairwise different widths. Several...