2016/10/03 by Michael Tait, Tait, Michael
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO
paper · pdf · doi:10.48550/arxiv.1610.00372
arxiv created 2016/10/03 · arxiv updated 2016/10/04
Let H\xrightarrows G denote that any s-coloring of E(H) contains a monochromatic G. The degree Ramsey number of a graph G, denoted by RΔ(G, s), is min \Δ(H): H \xrightarrows G \. We consider degree Ramsey numbers where G is a fixed even cycle. Kinnersley, Milans, and West showed that RΔ(C2k,s) ≥ 2s, and Kang and Perarnau showed that RΔ(C4, s) = Θ(s2). Our main result is that RΔ(C6, s) = Θ(s3/2) and RΔ(C10, s) = Θ(s5/4). Additionally, we substantially improve the lower bound for RΔ(C2k, s) for general k.