Large Monochromatic Components in Edge Colorings of Graphs: A Survey

@inproceedings{Gyrfs2011LargeMC,
  title={Large Monochromatic Components in Edge Colorings of Graphs: A Survey},
  author={Andr{\'a}s Gy{\'a}rf{\'a}s},
  year={2011}
}
The aim of this survey is to summarize an area of combinatorics that lies on the border of several areas: Ramsey theory, resolvable block designs, factorizations, fractional matchings and coverings, and partition covers. 
Ramsey-Type Problems for Geometric Graphs
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Given a k-colouring of the edges of the complete graph Kn, are there k-1 monochromatic components that cover its vertices? This important special case of the well-known Lov?sz-Ryser conjecture is
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. Given an r -edge-coloring of the complete graph K n , what is the largest number of edges in a monochromatic connected component? This natural question has only recently received the attention it
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This note improves the result in the case of r = 3 and shows that in every 3-edge-coloring of Kn either there is a monochromatic component of diameter at most three on at least n/2 vertices or every color class is spanning and has diameter at least four.
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