Supersaturation ofC4: From Zarankiewicz towards Erdős–Simonovits–Sidorenko
نویسندگان
چکیده
منابع مشابه
On 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 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 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 کاملCrystal Nucleation without Supersaturation.
Classical nucleation theory (CNT) has been extensively employed to interpret crystal nucleation phenomena and postulates the formation of an ordered crystalline nucleus directly from vapor or solution. Here, we provide the first experimental demonstration of a two-step mechanism that facilitates deposition of crystals on solid surfaces from vapor. Crucially, this occurs from saturated vapor wit...
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: European Journal of Combinatorics
سال: 2019
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2018.07.015