# Finding Large p-Colored Diameter Two Subgraphs

@article{Erds1999FindingLP, title={Finding Large p-Colored Diameter Two Subgraphs}, author={Paul Erd{\"o}s and Tom Fowler}, journal={Graphs and Combinatorics}, year={1999}, volume={15}, pages={21-27} }

Abstract. Given a coloring of the edges of the complete graph K on n vertices in k colors, a p-colored subgraph of Kn is any subgraph whose edges only use colors from some p element set. We show for k≥1 and k\2≤p≤k that there is always a p-colored diameter two subgraph of Kn containing at least vertices and that this is best possible up to an additive constant l satisfying 0≤l

## 13 Citations

Monochromatic diameter-2 components in edge colorings of the complete graph

- MathematicsInvolve, a Journal of Mathematics
- 2021

Gyarfas conjectured that in every r -edge-coloring of the complete graph K n there is a monochromatic component on at least n ∕ ( r − 1 ) vertices which has diameter at most 3. We show that for r = 3…

Size of Monochromatic Double Stars in Edge Colorings

- MathematicsGraphs Comb.
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- MathematicsJ. Graph Theory
- 2022

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.

Large components in r‐edge‐colorings of Kn have diameter at most five

- MathematicsJ. Graph Theory
- 2012

It is shown in this note that every r-edge-coloring of Kn contains a monochromatic component of diameter at most five on at least n/(r−1) vertices.

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- Mathematics
- 2010

A Gallai-coloring of a complete graph is an edge coloring such that no triangle is colored with three distinct colors. Gallai-colorings occur in various contexts such as the theory of partially…

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- 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,…

Ramsey‐type results for Gallai colorings

- MathematicsJ. Graph Theory
- 2010

It is proved that in every G-coloring of Kn there exists each of the following: a monochromatic double star with at least 3n+1 4 vertices; and RG(r,K3) can be determined exactly.

Rainbow Generalizations of Ramsey Theory - A Dynamic Survey

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- 2014

In this work, we collect Ramsey-type results concerning rainbow edge colorings of graphs. Revision History • Revision 3: March, 2015. • Revision 2: October, 2014. • Revision 1: July, 2011. •…

Rainbow Generalizations of Ramsey Theory: A Survey

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- 2010

In this work, Ramsey-type results concerning rainbow edge colorings of graphs are collected.

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