# Helly-type theorems for the ordering of the vertices of a hypergraph

@inproceedings{Biro2022HellytypeTF, title={Helly-type theorems for the ordering of the vertices of a hypergraph}, author={Csaba Bir'o and JenHo Lehel and G'eza T'oth}, year={2022} }

. Let H be a complete r -uniform hypergraph such that two vertices are marked in each edge as its ‘boundary’ vertices. A linear ordering of the vertex set of H is called an agreeing linear order , provided all vertices of each edge of H lie between its two boundary vertices. We prove the following Helly-type theorem: if there is an agreeing linear order on the vertex set of every subhypergraph of H with at most 2 r − 2 vertices, then there is an agreeing linear order on the vertex set of H . We…

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