On a combinatorical problem of K. Zarankiewicz
نویسندگان
چکیده
منابع مشابه
More on a Problem of Zarankiewicz
We show tight necessary and sufficient conditions on the sizes of small bipartite graphs whose union is a larger bipartite graph that has no large bipartite independent set. Our main result is a common generalization of two classical results in graph theory: the theorem of Kővári, Sós and Turán on the minimum number of edges in a bipartite graph that has no large independent set, and the theore...
متن کاملOn Zarankiewicz Problem and Depth-Two Superconcentrators
We show tight necessary and sufficient conditions on the sizes of small bipartite graphs whose union is a larger bipartite graph that has no large bipartite independent set. Our main result is a common generalization of two classical results in graph theory: the theorem of Kővári, Sós and Turán on the minimum number of edges in a bipartite graph that has no large independent set, and the theore...
متن کاملOn the Zarankiewicz Problem for Intersection Hypergraphs
Let d and t be fixed positive integers, and let K t,...,t denote the complete d-partite hypergraph with t vertices in each of its parts, whose hyperedges are the d-tuples of the vertex set with precisely one element from each part. According to a fundamental theorem of extremal hypergraph theory, due to Erdős [7], the number of hyperedges of a d-uniform hypergraph on n vertices that does not co...
متن کاملA contribution to the Zarankiewicz problem
Given positive integers m,n, s, t, let z (m,n, s, t) be the maximum number of ones in a (0, 1) matrix of size m× n that does not contain an all ones submatrix of size s× t. We show that if s ≥ 2 and t ≥ 2, then for every k = 0, . . . , s− 2, z (m,n, s, t) ≤ (s− k − 1) nm + kn+ (t− 1)m. This generic bound implies the known bounds of Kövari, Sós and Turán, and of Füredi. As a consequence, we also...
متن کاملOn the half?half case of the Zarankiewicz problem
Consider the minimum number f(m,n) of zeroes in a 2m×2n (0, 1)-matrixM that contains no m×n submatrix of ones. This special case of the well-known Zarankiewicz problem was studied by Griggs and Ouyang, who showed, for m ≤ n, that 2n+m+1 ≤ f(m,n) ≤ 2n + 2m − gcd(m,n) + 1. The lower bound is sharp when m is fixed for all large n. They proposed determining limm→∞{f(m,m+ 1)/m}. In this paper, we sh...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 1963
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-11-1-81-84