Clemens, DennisDennisClemensJenssen, MatthewMatthewJenssenKohayakawa, YoshiharuYoshiharuKohayakawaMorrison, NatashaNatashaMorrisonMota, Guilherme OliveiraGuilherme OliveiraMotaReding, DamianDamianRedingRoberts, BarnabyBarnabyRoberts2019-06-112019-06-112019-07Journal of Graph Theory 3 (91): 290-299 (2019-07)http://hdl.handle.net/11420/2755Given graphs G and H and a positive integer q, say that G is q-Ramsey for H, denoted G → (H) q , if every q-coloring of the edges of G contains a monochromatic copy of H. The size-Ramsey number (Formula presented.) of a graph H is defined to be (Formula presented.). Answering a question of Conlon, we prove that, for every fixed k, we have (Formula presented.), where P nk is the kth power of the n-vertex path P n (ie, the graph with vertex set V(P n ) and all edges u, v such that the distance between u and v in P n is at most k). Our proof is probabilistic, but can also be made constructive.en0364-902420193290299Journal Article10.1002/jgt.22432Other