Embedding arbitrary edge-colorings of hypergraphs into regular colorings
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909317852037120 |
|---|---|
| author | Wang, Xiaomiao Feng, Tao Wang, Shixin |
| author_facet | Wang, Xiaomiao Feng, Tao Wang, Shixin |
| contents | For $\textbf{r}=(r_1,\ldots,r_k)$, an $\textbf{r}$-factorization of the complete $λ$-fold $h$-uniform $n$-vertex hypergraph $λK_n^h$ is a partition of the edges of $λK_n^h$ into $F_1,\ldots, F_k$ such that $F_j$ is $r_j$-regular and spanning for $1\leq j\leq k$. This paper shows that for $n>\frac{m-1}{1-2^{\frac{1}{1-h}}}+h-1$, a partial $\textbf{r}$-factorization of $λK_m^h$ can be extended to an $\textbf{r}$-factorization of $λK_n^h$ if and only if the obvious necessary conditions are satisfied. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_10950 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Embedding arbitrary edge-colorings of hypergraphs into regular colorings Wang, Xiaomiao Feng, Tao Wang, Shixin Combinatorics For $\textbf{r}=(r_1,\ldots,r_k)$, an $\textbf{r}$-factorization of the complete $λ$-fold $h$-uniform $n$-vertex hypergraph $λK_n^h$ is a partition of the edges of $λK_n^h$ into $F_1,\ldots, F_k$ such that $F_j$ is $r_j$-regular and spanning for $1\leq j\leq k$. This paper shows that for $n>\frac{m-1}{1-2^{\frac{1}{1-h}}}+h-1$, a partial $\textbf{r}$-factorization of $λK_m^h$ can be extended to an $\textbf{r}$-factorization of $λK_n^h$ if and only if the obvious necessary conditions are satisfied. |
| title | Embedding arbitrary edge-colorings of hypergraphs into regular colorings |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2409.10950 |