On generalized Ramsey numbers

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 f2(G) n. 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 . Key words and phrases: Ramsey number, mixed Ramsey number. AMS 1991 Subject Classifications: 05C55

• Type: Journal
• Year: 2002
• Where: DM
• Authors: Wai Chee Shiu, Peter Che Bor Lam, Yusheng Li
• Keywords: DM 2002, General Existence Condition, General Upper Bound, Ramsey Number