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research-article

Large Y 3, 2-tilings in 3-uniform hypergraphs

Published: 24 July 2024 Publication History

Abstract

Let Y 3, 2 be the 3-graph with two edges intersecting in two vertices. We prove that every 3-graph H on n vertices with at least max 4 α n 3, n 3 − n − α n 3 + o ( n 3 ) edges contains a Y 3, 2-tiling covering more than 4 α n vertices, for sufficiently large n and 0 < α < 1 / 4. The bound on the number of edges is asymptotically best possible and solves a conjecture of the authors for 3-graphs that generalizes the Matching Conjecture of Erdős.

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Published In

cover image European Journal of Combinatorics
European Journal of Combinatorics  Volume 120, Issue C
Aug 2024
674 pages

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Academic Press Ltd.

United Kingdom

Publication History

Published: 24 July 2024

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