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Norm-graphs and bipartite turán numbers

✍ Scribed by János Kollár; Lajos Rónyai; Tibor Szabó

Publisher: Springer-Verlag
Year: 1996
Tongue: English
Weight: 384 KB
Volume: 16
Category: Article
ISSN: 0209-9683
DOI: 10.1007/bf01261323

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New Asymptotics for Bipartite Turán Numb

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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] an

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## 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 _

Upper Bounds for Turán Numbers

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A system of r-element subsets (blocks) of an n-element set X n is called a Tura n (n, k, r)-system if every k-element subset of X n contains at least one of the blocks. The Tura n number T(n, k, r) is the minimum size of such a system. We prove upper estimates: + as n Ä , r Ä , k=(#+o(1))r, #>1.

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## Abstract The minimum size of a __k__‐connected graph with given order and stability number is investigated. If no connectivity is required, the answer is given by Turán's Theorem. For connected graphs, the problem has been solved recently independently by Christophe et al., and by Gitler and Val