Antifactors in bipartite multigraphs
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2022
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913063339294720 |
|---|---|
| author | Esperet, Louis |
| author_facet | Esperet, Louis |
| contents | Let $G$ be a $q$-regular bipartite graph with bipartition $(U,V)$. It was proved by Lu, Wang, and Yan in 2020 that $G$ has a spanning subgraph $H$ such that each vertex of $U$ has degree 1 in $H$, and each vertex of $V$ has degree distinct from 1 in $H$. We extend the result to multigraphs, under the condition that $q$ is a prime power and the number of perfect matchings of $G$ is not divisible by $q$. The condition on the number of perfect matchings is necessary for multigraphs.
We conclude with a conjecture on the limiting distribution of the number of perfect matchings modulo $q$ in a random bipartite $q$-regular graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_14904 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Antifactors in bipartite multigraphs Esperet, Louis Combinatorics Let $G$ be a $q$-regular bipartite graph with bipartition $(U,V)$. It was proved by Lu, Wang, and Yan in 2020 that $G$ has a spanning subgraph $H$ such that each vertex of $U$ has degree 1 in $H$, and each vertex of $V$ has degree distinct from 1 in $H$. We extend the result to multigraphs, under the condition that $q$ is a prime power and the number of perfect matchings of $G$ is not divisible by $q$. The condition on the number of perfect matchings is necessary for multigraphs. We conclude with a conjecture on the limiting distribution of the number of perfect matchings modulo $q$ in a random bipartite $q$-regular graph. |
| title | Antifactors in bipartite multigraphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2205.14904 |