Loose Hamilton paths in the 3-uniform cube hypergraph
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916391514275840 |
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| author | Cooley, Oliver Machata, Johannes Pasch, Matija |
| author_facet | Cooley, Oliver Machata, Johannes Pasch, Matija |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_00401 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Loose Hamilton paths in the 3-uniform cube hypergraph Cooley, Oliver Machata, Johannes Pasch, Matija Combinatorics 05C38 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. |
| title | Loose Hamilton paths in the 3-uniform cube hypergraph |
| topic | Combinatorics 05C38 |
| url | https://arxiv.org/abs/2406.00401 |