A contribution to the Zarankiewicz problem
نویسندگان
چکیده
منابع مشابه
A 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 کاملSpectral Extrema for Graphs: The Zarankiewicz Problem
Let G be a graph on n vertices with spectral radius λ (this is the largest eigenvalue of the adjacency matrix of G). We show that if G does not contain the complete bipartite graph Kt,s as a subgraph, where 2 6 t 6 s, then λ 6 (
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 کاملMore 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 کاملThe Zarankiewicz problem in 3-partite graphs
Let F be a graph, k ≥ 2 be an integer, and write exχ≤k(n, F ) for the maximum number of edges in an n-vertex graph that is k-partite and has no subgraph isomorphic to F . The function exχ≤2(n, F ) has been studied by many researchers. Finding exχ≤2(n,Ks,t) is a special case of the Zarankiewicz problem. We prove an analogue of the Kövári-Sós-Turán Theorem by showing exχ≤3(n,Ks,t) ≤ ( 1 3 )1−1/s(...
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: Linear Algebra and its Applications
سال: 2010
ISSN: 0024-3795
DOI: 10.1016/j.laa.2009.10.040