A bipartite Ramsey problem and the Zarankiewicz numbers
نویسندگان
چکیده
منابع مشابه
Zarankiewicz Numbers and Bipartite Ramsey Numbers
The Zarankiewicz number z(b; s) is the maximum size of a subgraph of Kb,b which does not contain Ks,s as a subgraph. The two-color bipartite Ramsey number b(s, t) is the smallest integer b such that any coloring of the edges of Kb,b with two colors contains a Ks,s in the rst color or a Kt,t in the second color.In this work, we design and exploit a computational method for bounding and computing...
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The Zarankiewicz number z(s, m) is the maximum number of edges in a subgraph of K(s, s) that does not contain K(m, m) as a subgraph. The bipartite Ramsey number b(m, n) is the least positive integer b such that if the edges of K(b, b) are coloured with red and blue, then there always exists a blue K(m, m) or a red K(n, n). In this paper we calculate small exact values of z(s, 2) and determine b...
متن کاملzarankiewicz numbers and bipartite ramsey numbers
the zarankiewicz number z(b; s) is the maximum size of a subgraph of kb,b which does not contain ks,s as a subgraph. the two-color bipartite ramsey number b(s, t) is the smallest integer b such that any coloring of the edges of kb,b with two colors contains a ks,s in the rst color or a kt,t in the second color.in this work, we design and exploit a computational method for bounding and computin...
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The Zarankiewicz number z(m,n; s, t) is the maximum number of edges in a subgraph of Km,n that does not contain Ks,t as a subgraph. The bipartite Ramsey number b(n1, · · · , nk) is the least positive integer b such that any coloring of the edges of Kb,b with k colors will result in a monochromatic copy of Kni,ni in the i-th color, for some i, 1 ≤ i ≤ k. If ni = m for all i, then we denote this ...
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Let G and H be graphs. A graph with colored edges is said to be monochromatic if all its edges have the same color and rainbow if no two of its edges have the same color. Given two bipartite graphs G1 and G2, the bipartite rainbow ramsey number BRR(G1; G2) is the smallest integer N such that any coloring of the edges of KN;N with any number of colors contains a monochromatic copy of G1 or a rai...
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ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 1978
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089500003323