Norm-graphs and bipartite Turán numbers

János Kollár; Lajos Rónyai; Tibor Szabó

doi:10.1007/bf01261323

Norm-graphs and bipartite Turán numbers

János Kollár, Lajos Rónyai, Tibor Szabó

Research output: Contribution to journal › Article › peer-review

113 Scopus citations

Abstract

For every t > 1 and positive n we construct explicit examples of graphs G with |V(G)| = n, |E(G)| ≥ c_t · n^2-1/t which do not contain a complete bipartite graph K_t,t!+1. This establishes the exact order of magnitude of the Turán numbers ex(n,K_t,s) for any fixed t and all s ≥ t! + 1, improving over the previous probabilistic lower bounds for such pairs (t,s). The construction relies on elementary facts from commutative algebra.

Original language	English (US)
Pages (from-to)	399-406
Number of pages	8
Journal	Combinatorica
Volume	16
Issue number	3
DOIs	https://doi.org/10.1007/bf01261323
State	Published - 1996
Externally published	Yes

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics
Computational Mathematics

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10.1007/bf01261323

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AU - Szabó, Tibor

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AB - For every t > 1 and positive n we construct explicit examples of graphs G with |V(G)| = n, |E(G)| ≥ ct · n2-1/t which do not contain a complete bipartite graph Kt,t!+1. This establishes the exact order of magnitude of the Turán numbers ex(n,Kt,s) for any fixed t and all s ≥ t! + 1, improving over the previous probabilistic lower bounds for such pairs (t,s). The construction relies on elementary facts from commutative algebra.

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Norm-graphs and bipartite Turán numbers

Abstract

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