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Threshold Ramsey multiplicity for odd cycles
Volume 64, no. 1
(2022),
pp. 49–68
https://doi.org/10.33044/revuma.2874
Abstract
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 $K_n$ 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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Published by the Unión Matemática Argentina |
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