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2021 Monochromatic diameter-2 components in edge colorings of the complete graph
Miklós Ruszinkó, Lang Song, Daniel P. Szabo
Involve 14(3): 377-386 (2021). DOI: 10.2140/involve.2021.14.377

Abstract

Gyárfás 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 , 4 , 5 and 6 a diameter of 3 is best possible in this conjecture, constructing colorings where every monochromatic diameter-2 subgraph has strictly less than n ( r 1 ) vertices.

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Miklós Ruszinkó. Lang Song. Daniel P. Szabo. "Monochromatic diameter-2 components in edge colorings of the complete graph." Involve 14 (3) 377 - 386, 2021. https://doi.org/10.2140/involve.2021.14.377

Information

Received: 14 November 2019; Accepted: 17 January 2021; Published: 2021
First available in Project Euclid: 30 July 2021

Digital Object Identifier: 10.2140/involve.2021.14.377

Subjects:
Primary: 05C15, 05C51, 05C55, 05D10

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.14 • No. 3 • 2021
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