2023/02/27 by Zhang, Yanbo, Zhang, Yixin · 1 citation
#05C55 #05C57 #05D10 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2302.13640
For two graphs G1 and G2, the online Ramsey number r(G1,G2) is the smallest number of edges that Builder draws on an infinite empty graph to guarantee that there is either a red copy of G1 or a blue copy of G2, under the condition that Builder draws one edge in each round and Painter immediately colors it red or blue. For online Ramsey numbers of paths, Cyman, Dzido, Lapinskas, and Lo conjectured that r(P4, Pℓ+1) = \lceil(7ℓ+2)/5\rceil for all ℓ ≥ 3 [Electron. J. Combin. 22 (2015) #P1.15]. We verify the conjecture in this paper.