A lower bound for irredundant Ramsey numbers
نویسندگان
چکیده
منابع مشابه
A Lower Bound for Schur Numbers and Multicolor Ramsey Numbers
For k ≥ 5, we establish new lower bounds on the Schur numbers S(k) and on the k-color Ramsey numbers of K3. For integers m and n, let [m,n] denote the set {i |m ≤ i ≤ n}. A set S of integers is called sum-free if i, j ∈ S implies i + j 6∈ S, where we allow i = j. The Schur function S(k) is defined for all positive integers as the maximum n such that [1, n] can be partitioned into k sum-free set...
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The Ramsey number R(G1; G2; : : : ; Gn) is the smallest integer p such that for any n-edge coloring (E1; E2; : : : ; En) of Kp; Kp[Ei] contains Gi for some i, Gi as a subgraph in Kp[Ei]. Let R(m1; m2; : : : ; mn):=R(Km1 ; Km2 ; : : : ; Kmn); R(m; n):=R(m1; m2; : : : ; mn) if mi=m for i=1; 2; : : : ; n. A formula is obtained for R(G1; G2; : : : ; Gn). c © 2001 Elsevier Science B.V. All rights re...
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The Ramsey number r(H,G) is defined as the minimum N such that for any coloring of the edges of the N -vertex complete graph KN in red and blue, it must contain either a red H or a blue G. In this paper we show that for any graph G without isolated vertices, r(K3, G) ≤ 2q + 1 where G has q edges. In other words, any graph on 2q + 1 vertices with independence number at most 2 contains every (iso...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1998
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(97)00055-1