TY - JOUR

T1 - THRESHOLD RAMSEY MULTIPLICITY FOR ODD CYCLES

AU - Conlon, David

AU - Fox, Jacob

AU - Sudakov, Benny

AU - Wei, Fan

N1 - Funding Information:
The first author is supported by NSF Award DMS-2054452. The second author is supported by a Packard Fellowship and by NSF Award DMS-1855635. The third author is supported by SNSF grant 200021 196965. The last author is supported by NSF Award DMS-1953958.
Publisher Copyright:
© 2022,Revista de la Union Matematica Argentina.All Rights Reserved

PY - 2022

Y1 - 2022

N2 - 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-edgecolorings of Kr(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.

AB - 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-edgecolorings of Kr(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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U2 - 10.33044/revuma.2874

DO - 10.33044/revuma.2874

M3 - Article

AN - SCOPUS:85137684382

SN - 0041-6932

VL - 64

SP - 49

EP - 68

JO - Revista de la Union Matematica Argentina

JF - Revista de la Union Matematica Argentina

IS - 1

ER -