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Vertex coverings by monochromatic cycles and trees
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 relatedExpand
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A variant of the classical Ramsey problem
We show that certain special cases of the problem closely relate to Turán type hypergraph problems introduced by Brown, Erdős and T. Sós. Expand
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On-line and first fit colorings of graphs
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
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Edge colorings of complete graphs without tricolored triangles
We show some consequences of results of Gallai concerning edge colorings of complete graphs that contain no tricolored triangles. Expand
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An improved bound for the monochromatic cycle partition number
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
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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 thatExpand
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Coloring the Maximal Cliques of Graphs
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
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Covering and coloring problems for relatives of intervals
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
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