TY - JOUR

T1 - On generalized Ramsey numbers

AU - SHIU, Wai Chee

AU - Lam, Peter Che Bor

AU - Li, Yusheng

N1 - Funding Information:
Partially supported by RGC, Hong Kong; FRG, Hong Kong Baptist University; and by NSFC and a scienti5c foundation of education ministry of China. ∗Corresponding author. E-mail addresses: [email protected] (W.C. Shiu), [email protected] (P.C.B. Lam), [email protected] (Y. Li).

PY - 2002/12/6

Y1 - 2002/12/6

N2 - 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(Ḡ) ≥ 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 → ∞.

AB - 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(Ḡ) ≥ 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 → ∞.

KW - Mixed ramsey number

KW - Ramsey number

UR - http://www.scopus.com/inward/record.url?scp=0037032972&partnerID=8YFLogxK

U2 - 10.1016/S0012-365X(02)00540-X

DO - 10.1016/S0012-365X(02)00540-X

M3 - Journal article

AN - SCOPUS:0037032972

SN - 0012-365X

VL - 258

SP - X383-388

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 1-3

ER -