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- W1555444037 abstract "Let $Q(n,c)$ denote the minimum clique number over graphs with $n$ vertices and chromatic number $c$. We investigate the asymptotics of $Q(n,c)$ when $n/c$ is held constant. We show that when $n/c$ is an integer $alpha$, $Q(n,c)$ has the same growth order as the inverse function of the Ramsey number $R(alpha+1,t)$ (as a function of $t$). Furthermore, we show that if certain asymptotic properties of the Ramsey numbers hold, then $Q(n,c)$ is in fact asymptotically equivalent to the aforementioned inverse function. We use this fact to deduce that $Q(n,lceil n/3 rceil)$ is asymptotically equivalent to the inverse function of $R(4,t)$." @default.
- W1555444037 created "2016-06-24" @default.
- W1555444037 creator A5071557296 @default.
- W1555444037 date "2012-03-19" @default.
- W1555444037 modified "2023-09-29" @default.
- W1555444037 title "Minimum Clique Number, Chromatic Number, and Ramsey Numbers" @default.
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- W1555444037 doi "https://doi.org/10.37236/2125" @default.
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