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A variant of the classical Ramsey problem
TLDR
The Local Lemma is used to give a general upper bound forf, and it is shown that certain special cases of the problem closely relate to Turán type hypergraph problems introduced by Brown, Erdős and T. Sós.
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. We prove two conjectures of Bialostocki and Voxman about the
On-line and first fit colorings of graphs
TLDR
An upper bound for the performance ratio of the first fit coloring on interval graphs is proved and it is shown that there are simple families resisting any on-line algorithm: no on- line algorithm can color all trees by a bounded number of colors.
Coloring the Maximal Cliques of Graphs
TLDR
It is shown that "almost" all perfect graphs are 3-clique-colorable, and exact bounds and polynomial algorithms that find the clique-chromatic number for some classes of graphs are shown and NP-completeness results for some others are proved.
Three-Color Ramsey Numbers For Paths
TLDR
It is proved that for sufficiently large n, for the three-color Ramsey numbers of paths on n vertices, the following conjecture of Faudree and Schelp is proved.
THE STRONG CHROMATIC INDEX OF GRAPHS
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
Vertex coverings by monochromatic paths and cycles
TLDR
The role of results on covering the vertices of 2-colored complete graphs by two paths or by two cycles of different color in determining path Ramsey numbers and in algorithms for finding long monochromatic paths or cycles in 2- colored complete graphs is shown.
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