Anti-Ramsey numbers of loose paths and cycles in uniform hypergraphs
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929337160171520 |
|---|---|
| author | Li, Tong Tang, Yucong Wang, Guanghui Yan, Guiying |
| author_facet | Li, Tong Tang, Yucong Wang, Guanghui Yan, Guiying |
| contents | For a fixed family of $r$-uniform hypergraphs $\mathcal{F}$, the anti-Ramsey number of $\mathcal{F}$, denoted by $ ar(n,r,\mathcal{F})$, is the minimum number $c$ of colors such that for any edge-coloring of the complete $r$-uniform hypergraph on $n$ vertices with at least $c$ colors, there is a rainbow copy of some hypergraph in $\mathcal{F}$. Here, a rainbow hypergraph is an edge-colored hypergraph with all edges colored differently. Let $\mathcal{P}_k$ and $\mathcal{C}_k$ be the families of loose paths and loose cycles with $k$ edges in an $r$-uniform hypergraph, respectively. In this paper, we determine the exact values of $ ar(n,r,\mathcal{P}_k)$ and $ ar(n,r,\mathcal{C}_k)$ for all $k\geq 4$ and $r\geq 3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04349 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Anti-Ramsey numbers of loose paths and cycles in uniform hypergraphs Li, Tong Tang, Yucong Wang, Guanghui Yan, Guiying Combinatorics For a fixed family of $r$-uniform hypergraphs $\mathcal{F}$, the anti-Ramsey number of $\mathcal{F}$, denoted by $ ar(n,r,\mathcal{F})$, is the minimum number $c$ of colors such that for any edge-coloring of the complete $r$-uniform hypergraph on $n$ vertices with at least $c$ colors, there is a rainbow copy of some hypergraph in $\mathcal{F}$. Here, a rainbow hypergraph is an edge-colored hypergraph with all edges colored differently. Let $\mathcal{P}_k$ and $\mathcal{C}_k$ be the families of loose paths and loose cycles with $k$ edges in an $r$-uniform hypergraph, respectively. In this paper, we determine the exact values of $ ar(n,r,\mathcal{P}_k)$ and $ ar(n,r,\mathcal{C}_k)$ for all $k\geq 4$ and $r\geq 3$. |
| title | Anti-Ramsey numbers of loose paths and cycles in uniform hypergraphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2405.04349 |