A set of vertices in a graph is a dominating set if every vertex outside the set has a neighbor in the set. The domatic number problem is that of partitioning the vertices of a gra...
Heuristic algorithms for coloring the edges of large undirected single-edge graphs with (or very close to) the minimal number of colors are presented. Compared to simulated anneal...
Mario Hilgemeier, Nicole Drechsler, Rolf Drechsler
The visibility graph V(X) of a discrete point set X R2 has vertex set X and an edge xy for every two points x, y X whenever there is no other point in X on the line segment betw...
A k-frugal colouring of a graph G is a proper colouring of the vertices of G such that no colour appears more than k times in the neighbourhood of a vertex. This type of colouring...
We show that a random 4-regular graph asymptotically almost surely (a.a.s.) has chromatic number 3. The proof uses an efficient algorithm which a.a.s. 3colours a random 4-regular ...