|Publisher DOI:||10.1002/jgt.22432||Title:||The size-Ramsey number of powers of paths||Language:||English||Authors:||Clemens, Dennis
Mota, Guilherme Oliveira
|Issue Date:||Jul-2019||Source:||Journal of Graph Theory 3 (91): 290-299 (2019-07)||Journal or Series Name:||Journal of graph theory||Abstract (english):||
Given 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.
|URI:||http://hdl.handle.net/11420/2755||ISSN:||0364-9024||Institute:||Mathematik E-10||Document Type:||Article|
|Appears in Collections:||Publications without fulltext|
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