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arXiv · 2103.13571

Shadows of 3-uniform hypergraphs under a minimum degree condition

Zoltán Füredi·Yi Zhao
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Abstract

We prove a minimum degree version of the Kruskal--Katona theorem: given $d\ge 1/4$ and a triple system $F$ on $n$ vertices with minimum degree at least $d\binom n2$, we obtain asymptotically tight lower bounds for the size of its shadow. Equivalently, for $t\ge n/2-1$, we asymptotically determine the minimum size of a graph on $n$ vertices, in which every vertex is contained in at least $\binom t2$ triangles. This can be viewed as a variant of the Rademacher--Turán problem.

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Zoltán Füredi, Yi Zhao. 2022-07-17. Shadows of 3-uniform hypergraphs under a minimum degree condition. https://arxiv.org/abs/2103.13571

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