... becomes the desired path For comparison with degree Ramsey number, note that R∆ (Pk ) = for k ≥ ([26] and [1] combined), while R∆ (K1,m ) equals 2m − for odd m and 2m − for even m [5] the electronic ... P Horn, K.G Milans, and V R¨dl, Degree Ramsey numbers for blowups of trees, o draft [15] T Jiang, K.G Milans, and D.B West, Degree Ramsey number of cycles is bounded, submitted [16] H.A Kierstead ... Coloring number and on-line Ramsey theory for graphs and hypergraphs Combinatorica 29 (2009), 49–64 [17] W.B Kinnersley, Multicolor on-line degree Ramsey numbers for trees and cycles, draft [18]...