Matchings in the hypercube with specified edges
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866918534695616512 |
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| author | Erde, Joshua |
| author_facet | Erde, Joshua |
| contents | Given a matching $M$ in the hypercube $Q^n$, the \emph{profile} of $M$ is the vector $\boldsymbol{x}=(x_1,\ldots, x_n) \in \mathbb{N}^n$ such that $M$ contains $x_i$ edges whose endpoints differ in the $i$th coordinate. If $M$ is a perfect matching, then it is clear that $||\boldsymbol{x}||_1 = 2^{n-1}$ and it is easy to show that each $x_i$ must be even. Verifying a special case of a conjecture of Balister, Győri, and Schelp, we show that these conditions are also sufficient. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03950 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Matchings in the hypercube with specified edges Erde, Joshua Combinatorics Given a matching $M$ in the hypercube $Q^n$, the \emph{profile} of $M$ is the vector $\boldsymbol{x}=(x_1,\ldots, x_n) \in \mathbb{N}^n$ such that $M$ contains $x_i$ edges whose endpoints differ in the $i$th coordinate. If $M$ is a perfect matching, then it is clear that $||\boldsymbol{x}||_1 = 2^{n-1}$ and it is easy to show that each $x_i$ must be even. Verifying a special case of a conjecture of Balister, Győri, and Schelp, we show that these conditions are also sufficient. |
| title | Matchings in the hypercube with specified edges |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2404.03950 |