Abstract If the edges of a finite complete graph K are colored with r colors then the vertex set of K can be covered by at most cr 2 log r vertex disjoint monochromatic cycles. Several related… Expand

A graph coloring algorithm that immediately colors the vertices taken from a list without looking ahead or changing colors already assigned is called an on-line coloring.Expand

Improving a result of Erdos, Gyarfas and Pyber for large n we show that for every integer r>=2 there exists a constant n"0=n"0(r) such that if the edges of the complete graph K"n are colored with r colors then the vertex set can be partitioned into at most 100rlogr vertex disjoint monochromatic cycles.Expand

Problems and results are presented concerning the strong chromatic index, where the strong chromatic index is the smallest k such that the edges of the graph can be k-colored with the property that… Expand

In this paper we are concerned with the so-called clique-colorations of a graph, that is, colorations of the vertices so that no maximal clique is monochromatic.Expand

We survey results and problems concerning the dependence of the transversal number on the packing number and the clique number in the intersection graphs of interval families.Expand