The circular arc coloring problem is to find a minimum coloring of a set of arcs of a circle so that no two overlapping arcs share a color. This N P-hard problem arises in a rich variety of applications and has been studied extensively. In this paper we present an O(n2m) combinatorial algorithm for optimally coloring any set of arcs that corresponds to a perfect graph, and propose a new approac...

the prevalent communications networks suffer from lack of spectrum and spectrum inefficiency. this has motivated researchers to develop cognitive radio (cr) as a smart and dynamic radio access promised solution. a major challenge to this new technology is how to make fair assignment of available spectrum to unlicensed users, particularly for smart grids communication. this paper introduces an i...

An incidence of G consists of a vertex and one of its incident edge in G. The incidence coloring problem is a variation of vertex coloring problem. The problem is to find the minimum number (called incidence coloring number) of colors assigned to every incidence of G so that the adjacent incidences are not assigned the same color. In this paper, we propose a linear time algorithm for incidence-...

In the minimum sum coloring problem, the goal is to color the vertices of a graph with the positive integers such that the sum of all colors is minimal. Recently, it was shown that coloring a graph by iteratively coloring maximum independent sets yields a 4 + o(1) approximation for the minimum sum coloring problem. In this note, we show that this bound is tight. We construct a graph for which t...

Efficiently coloring an arbitrary graph is a fundamental and notoriously difficult algorithmic problem. This talk focuses on the restricted problem of determining the complexity of coloring graphs which do not contain a certain induced subgraph. Combining results of Kamiński and Lozin, and Hoyler, it follows that this problem remains NP-complete unless the excluded induced subgraph is a disjoin...

In this note, we use a reduction by Cornaz and Jost from the graph (max-)coloring problem to the maximum (weighted) stable set problem in order to characterize new graph classes where the graph coloring problem and the more general max-coloring problem can be solved in polynomial time.