A note on the size Ramsey number of powers of paths

19 Sep 2019 You Chunlin

Let $r\geq3$ be an integer such that $r-2$ is a prime power and let $H$ be a connected graph on $n$ vertices with average degree at least $d$ and $\alpha(H)\leq\beta n$, where $0<\beta<1$ is a constant. We prove that the size Ramsey number \[ \hat{R}({H};r) > \frac{{nd}}{2}{(r - 2)^2} - C\sqrt n \] for all sufficiently large $n$, where $C$ is a constant depending only on $r$ and $d$... (read more)

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