Ramsey numbers involving a long path

Let H be a graph, and sigma (H) the minimum size of a color class among all proper vertex-coloring of H with x (H) colors. A connected graph G with vertical bar G vertical bar >= sigma(H) is said to be H-good if R(G, H) = (x(H) - 1)(vertical bar G vertical bar - 1) + sigma(H). In this note, we shall show that if n >= 8 vertical bar H vertical bar + 3 sigma(2)(H) + cx(8)(H), then P-n, is H-good, where c = 10(14). (c) 2015 Elsevier B.V. All rights reserved.