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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For given finite family of graphs G1, G2, . . . , Gk, k ≥ 2, the multicolor Ramsey number R(G1, G2, . . . , Gk) is the smallest integer n such that if we arbitrarily color the edges of the complete graph on n vertices with k colors then there is always a monochromatic copy of Gi colored with i, for some 1 ≤ i ≤ k. We give a lower bound for k−color Ramsey number R(Cm, Cm, . . . , Cm), where m ≥ ...
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متن کاملA bound for multicolor Ramsey numbers
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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ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2019
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.2151