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arXiv · 2310.05601

On forbidding graphs as traces of hypergraphs

Dániel Gerbner·Michael E. Picollelli
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Abstract

We say that a hypergraph $\mathcal{H}$ contains a graph $H$ as a trace if there exists some set $S\subset V(\mathcal{H})$ such that $\mathcal{H}|_S=\{h\cap S: h\in E(\mathcal{H})\}$ contains a subhypergraph isomorphic to $H$. We study the largest number of hyperedges in 3-uniform hypergraphs avoiding some graph $F$ as trace. In particular, we improve a bound given by Luo and Spiro in the case $F=C_4$, and obtain exact bounds for large $n$ when $F$ is a book graph.

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Dániel Gerbner, Michael E. Picollelli. 2025-03-11. On forbidding graphs as traces of hypergraphs. https://arxiv.org/abs/2310.05601

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