Publisher DOI: 10.1002/jgt.22432
Title: The size-Ramsey number of powers of paths
Language: English
Authors: Clemens, Dennis  
Jenssen, Matthew 
Kohayakawa, Yoshiharu 
Morrison, Natasha 
Mota, Guilherme Oliveira 
Reding, Damian 
Roberts, Barnaby 
Issue Date: Jul-2019
Source: Journal of Graph Theory 3 (91): 290-299 (2019-07)
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.
ISSN: 0364-9024
Institute: Mathematik E-10 
Document Type: Article
Journal: Journal of graph theory 
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