Finding Large p-Colored Diameter Two Subgraphs

  title={Finding Large p-Colored Diameter Two Subgraphs},
  author={Paul Erd{\"o}s and Tom Fowler},
  journal={Graphs and Combinatorics},
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 
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Rainbow Generalizations of Ramsey Theory - A Dynamic Survey
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. •
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Finding Large Monochromatic Diameter Two Subgraphs
Given a coloring of the edges of the complete graph on n vertices in k colors, by considering the neighbors of an arbitrary vertex it follows that there is a monochromatic diameter two subgraph on at
Intersection Theorems for Systems of Sets
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Let n and k be positive integers, k≥3. Denote by ϕ(n, k) the least positive integer such that if F is any family of more than ϕ(n, k) sets, each set with n elements, then some k members of F have
A Partition of two-colored complete graphs
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