On some Multicolor Ramsey Properties of Random Graphs

  title={On some Multicolor Ramsey Properties of Random Graphs},
  author={Andrzej Dudek and Paweł Prałat},
  journal={SIAM J. Discret. Math.},
The size-Ramsey number $\hat{R}(F)$ of a graph $F$ is the smallest integer $m$ such that there exists a graph $G$ on $m$ edges with the property that any colouring of the edges of $G$ with two colours yields a monochromatic copy of $F$. In this paper, first we focus on the size-Ramsey number of a path $P_n$ on $n$ vertices. In particular, we show that $5n/2-15/2 \le \hat{R}(P_n) \le 74n$ for $n$ sufficiently large. (The upper bound uses expansion properties of random $d$-regular graphs.) This… 
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