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arXiv · 1303.5022

Turán Numbers for Forests of Paths in Hypergraphs

Neal Bushaw·Nathan Kettle
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Abstract

The Turán number of an r-uniform hypergraph H is the maximum number of edges in any r-graph on n vertices which does not contain H as a subgraph. Let P_l^(r) denote the family of r-uniform loose paths on l edges, F(k,l) denote the family of hypergraphs consisting of k disjoint paths from P_l^(r), and P'_l^(r) denote an r-uniform linear path on l edges. We determine precisely ex_r(n;F(k,l)) and ex_r(n;k*P'_l^(r)), as well as the Turán numbers for forests of paths of differing lengths (whether these paths are loose or linear) when n is appropriately large dependent on k,l,r, for r>=3. Our results build on recent results of Füredi, Jiang, and Seiver who determined the extremal numbers for individual paths, and provide more hypergraphs whose Turan numbers are exactly determined.

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Neal Bushaw, Nathan Kettle. 2014-02-24. Turán Numbers for Forests of Paths in Hypergraphs. https://arxiv.org/abs/1303.5022

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