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Threshold Ramsey multiplicity for odd cycles

Conlon, David and Fox, Jacob and Sudakov, Benny and Wei, Fan (2022) Threshold Ramsey multiplicity for odd cycles. Revista de la Unión Matemática Argentina, 64 (1). pp. 49-68. ISSN 1669-9637. doi:10.33044/revuma.2874.

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The Ramsey number r(H) of a graph H is the minimum n such that any two-coloring of the edges of the complete graph Kₙ contains a monochromatic copy of H. The threshold Ramsey multiplicity m(H) is then the minimum number of monochromatic copies of H taken over all two-edge-colorings of K_(r(H)). The study of this concept was first proposed by Harary and Prins almost fifty years ago. In a companion paper, the authors have shown that there is a positive constant c such that the threshold Ramsey multiplicity for a path or even cycle with k vertices is at least (ck)ᵏ, which is tight up to the value of c. Here, using different methods, we show that the same result also holds for odd cycles with k vertices.

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Conlon, David0000-0001-5899-1829
Additional Information:The first author [Conlon] is supported by NSF Award DMS-2054452. The second author [Fox] is supported by a Packard Fellowship and by NSF Award DMS-1855635. The third author [Sudakov] is supported by SNSF grant 200021_196965. The last author [Wei] is supported by NSF Award DMS-1953958.
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Swiss National Science Foundation (SNSF)200021_196965
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Record Number:CaltechAUTHORS:20221107-997760900.3
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ID Code:117741
Deposited By: Research Services Depository
Deposited On:17 Nov 2022 18:47
Last Modified:17 Nov 2022 18:47

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