Vol. 14, No. 3, 2021

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

Miklós Ruszinkó, Lang Song and Daniel P. Szabo

Vol. 14 (2021), No. 3, 377–386
Abstract

Gyárfás conjectured that in every r-edge-coloring of the complete graph Kn 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.

Keywords
Ramsey theory, edge colorings, graph theory, combinatorics, monochromatic components, graph factorization
Mathematical Subject Classification 2010
Primary: 05C15, 05C51, 05C55, 05D10
Milestones
Received: 14 November 2019
Revised: 26 September 2020
Accepted: 17 January 2021
Published: 17 July 2021

Communicated by Ann N. Trenk
Authors
Miklós Ruszinkó
Alfréd Rényi Institute of Mathematics
Budapest
Hungary
Faculty of Information Technology and Bionics
Pázmány Péter Catholic University
Budapest
Hungary
Lang Song
Department of Mathematics
Grinnell College
Grinnell, IA
United States
Daniel P. Szabo
Department of Computer Science
University of Wisconsin
Madison, WI
United States