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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
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Abstract |
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Gyárfás conjectured that in every -edge-coloring of the complete graph there is a monochromatic component on at least vertices which has diameter at most 3. We show that for and a diameter of 3 is best possible in this conjecture, constructing colorings where every monochromatic diameter-2 subgraph has strictly less than vertices. |
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Keywords
Ramsey theory, edge colorings, graph theory, combinatorics,
monochromatic components, graph factorization
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Mathematical Subject Classification 2010
Primary: 05C15, 05C51, 05C55, 05D10
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Milestones
Received: 14 November 2019
Revised: 26 September 2020
Accepted: 17 January 2021
Published: 17 July 2021
Communicated by Ann N. Trenk
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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 |
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| Daniel P. Szabo | |
| Department of Computer Science University of Wisconsin Madison, WI United States |
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