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arXiv · 2406.00401

Loose Hamilton paths in the 3-uniform cube hypergraph

Oliver Cooley·Johannes Machata·Matija Pasch
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Abstract

It is well-known that the $d$-dimensional hypercube contains a Hamilton cycle for $d\ge 2$. In this paper we address the analogous problem in the $3$-uniform cube hypergraph, a $3$-uniform analogue of the hypercube: for simple parity reasons, the $3$-uniform cube hypergraph can never admit a loose Hamilton cycle in any dimension, so we do the next best thing and consider loose Hamilton paths, and determine for which dimensions these exist.

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Oliver Cooley, Johannes Machata, Matija Pasch. 2024-09-12. Loose Hamilton paths in the 3-uniform cube hypergraph. https://arxiv.org/abs/2406.00401

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