✦ LIBER ✦

New Asymptotics for Bipartite Turán Numbers

✍ Scribed by Zoltán Füredi

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 168 KB
Volume: 75
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.1996.0067

No coin nor oath required. For personal study only.

✦ Synopsis

An algebraic construction implies lim n Ä ex(n, K 2, t+1 ) n &3Â2 =-tÂ2. 1996 Academic Press, Inc. 1 2 -t n 3Â2 +(nÂ4). To prove the Theorem we obtain a matching lower bound from a construction closely related to the examples from [ERS] and [B], and inspired by an example of Hylte n Cavallius [H] and Mo rs [M] given for Zarankiewicz's problem z(n, n, 2, t+1) (see later in Section 3). The topic is so short of constructions that about 20 years ago, as a first step, Erdo s [E67, E75] even proposed the problem whether lim t (lim inf n ex(n, K 2, t+1 ) n &3Â2 ) goes to as t Ä . For a survey see Bolloba s' book [Bo].

📜 SIMILAR VOLUMES

On two Turán Numbers

✍ Jian Shen 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 85 KB

Mean Ramsey–Turán numbers

✍ Raphael Yuster 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 124 KB

## Abstract A ρ‐mean coloring of a graph is a coloring of the edges such that the average number of colors incident with each vertex is at most ρ. For a graph __H__ and for ρ ≥ 1, the __mean Ramsey–Turán number RT__(__n, H,ρ − mean__) is the maximum number of edges a ρ‐__mean__ colored graph with _

On the Turán Number of Triple Systems

✍ Dhruv Mubayi; Vojtêch Rödl 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 176 KB

For a family of r-graphs F; the Tur! a an number exðn; FÞ is the maximum number of edges in an n vertex r-graph that does not contain any member of F: The Tur! a an density When F is an r-graph, pðFÞ=0; and r > 2; determining pðFÞ is a notoriously hard problem, even for very simple r-graphs F: For

An Upper Bound for the Turán Number t3(n

An Upper Bound for the Turán Number t3(n, 4)

✍ Fan Chung; Linyuan Lu 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 117 KB

Let t r (n, r+1) denote the smallest integer m such that every r-uniform hypergraph on n vertices with m+1 edges must contain a complete graph on r+1 vertices. In this paper, we prove that lim 3+-17 12 =0.593592... .

A Ramsey-type problem and the Turán numb

A Ramsey-type problem and the Turán numbers

✍ N. Alon; P. Erdős; D. S. Gunderson; M. Molloy 📂 Article 📅 2002 🏛 John Wiley and Sons 🌐 English ⚖ 101 KB

## Abstract For each __n__ and __k__, we examine bounds on the largest number __m__ so that for any __k__‐coloring of the edges of __K~n~__ there exists a copy of __K~m~__ whose edges receive at most __k−__1 colors. We show that for $k \ge \sqrt{n}\;+\,\Omega(n^{1/3})$, the largest value of __m__ i

Turán problems for integer-weighted grap

Turán problems for integer-weighted graphs

✍ Zoltán Füredi; André Kündgen 📂 Article 📅 2002 🏛 John Wiley and Sons 🌐 English ⚖ 238 KB

## Abstract A multigraph is (__k__,__r__)‐dense if every __k__‐set spans at most __r__ edges. What is the maximum number of edges ex~ℕ~(__n__,__k__,__r__) in a (__k__,__r__)‐dense multigraph on __n__ vertices? We determine the maximum possible weight of such graphs for almost all __k__ and __r__ (e