Matchings in hypercubes extend to long cycles
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913795850371072 |
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| author | Fink, Jiří Mütze, Torsten |
| author_facet | Fink, Jiří Mütze, Torsten |
| contents | The $d$-dimensional hypercube graph $Q_d$ has as vertices all subsets of $\{1,\ldots,d\}$, and an edge between any two sets that differ in a single element. The Ruskey-Savage conjecture asserts that every matching of $Q_d$, $d\ge 2$, can be extended to a Hamilton cycle, i.e., to a cycle that visits every vertex exactly once. We prove that every matching of $Q_d$, $d\ge 2$, can be extended to a cycle that visits at least a $2/3$-fraction of all vertices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01769 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Matchings in hypercubes extend to long cycles Fink, Jiří Mütze, Torsten Combinatorics The $d$-dimensional hypercube graph $Q_d$ has as vertices all subsets of $\{1,\ldots,d\}$, and an edge between any two sets that differ in a single element. The Ruskey-Savage conjecture asserts that every matching of $Q_d$, $d\ge 2$, can be extended to a Hamilton cycle, i.e., to a cycle that visits every vertex exactly once. We prove that every matching of $Q_d$, $d\ge 2$, can be extended to a cycle that visits at least a $2/3$-fraction of all vertices. |
| title | Matchings in hypercubes extend to long cycles |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2401.01769 |