We exploit the close relationship between circular arc graphs and interval graphs to design efficient approximation algorithms for NP-hard Optimization problems on circular arc graphs. The problems considered here are maximum domatic partition and on-line minimum vertex coloring. We present a heuristic for the domatic partition problem with a performance ratio of 4. For on-line coloring, we con...

Let G = (V,E) be an undirected graph and let π = {V1, V2, . . . , Vk} be a partition of the vertices V of G into k blocks Vi. From this partition one can construct the following digraph D(π) = (π,E(π)), the vertices of which correspond one-to-one with the k blocks Vi of π, and there is an arc from Vi to Vj if every vertex in Vj is adjacent to at least one vertex in Vi, that is, Vi dominates Vj ...

A vertex v in a vertex-subset I of an undirected graph G is said to be redundant if its closed neighborhood is contained in the union of closed neighborhoods of vertices of I − {v}. In the context of a communication network , this means that any vertex that may receive communications from I may also be informed from I − {v} . The irredundance number ir(G) is the minimum cardinality taken over a...