Abstract
Let H be a graph, and σ(H) the minimum size of a color class among all proper vertex-coloring of H with χ(H) colors. A connected graph G with |G|≥σ(H) is said to be H-good if R(G,H)=(χ(H)−1)(|G|−1)+σ(H). In this note, we shall show that if n≥8|H|+3σ2(H)+cχ8(H), then Pn is H-good, where c=1014.
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