Abstract
Given two graphs G and H, the Ramsey numberR(G,H) is defined as the minimum number of vertices n such that every {red,blue}-edge-coloring of Kn contains either a red copy of G or a blue copy of H. If G≅H, then we write R(G) for short. For any positive integer k, the Gallai–Ramsey number grk(G:H) is the minimum number of vertices n such that any exact k-edge coloring of Kn contains either a rainbow copy of G or a monochromatic copy of H. In this paper, we give exact values or upper and lower bounds for Ramsey numbers R(Cbn), R(Sm), R(Sm,Cbn) and Gallai–Ramsey numbers grk(K1,3:Cbn), grk(K1,3:Sm), where Cbn and Sm are the comb and sun graphs, respectively.
Published Version
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