Department of Mathematics
Let f1 and f2 be graph parameters. The Ramsey number r(f1⩾m;f2⩾n) is defined as the minimum integer N such that any graph G on N vertices, either f1(G)⩾m or . A general existence condition is given and a general upper bound is shown in this paper. In addition, suppose the number of triangles in G is denoted by t(G). We verify that (1−o(1))(24n)1/3⩽r(t⩾n;t⩾n)⩽(1+o(1))(48n)1/3 as n→∞.
Ramsey number, Mixed Ramsey number
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Link to Publisher's Edition
Shiu, W., Lam, P., & Li, Y. (2002). On generalized Ramsey numbers. Discrete Mathematics, 258 (1-3). https://doi.org/10.1016/S0012-365X(02)00540-X