Edge-coloring $K_{n, n}$ with no 2-colored $C_{2k}$
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915396523655168 |
|---|---|
| author | Bal, Deepak Bennett, Patrick |
| author_facet | Bal, Deepak Bennett, Patrick |
| contents | The generalized Ramsey number $r(G, H, q)$ is the minimum number of colors needed to color the edges of $G$ such that every isomorphic copy of $H$ has at least $q$ colors. In this note, we improve the upper and lower bounds on $r(K_{n, n}, C_{2k}, 3)$. Our upper bound answers a question of Lane and Morrison. For $k=3$ we obtain the asymptotically sharp estimate $r(K_{n, n}, C_6, 3) = \frac{7}{20} n + o(n)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13329 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Edge-coloring $K_{n, n}$ with no 2-colored $C_{2k}$ Bal, Deepak Bennett, Patrick Combinatorics The generalized Ramsey number $r(G, H, q)$ is the minimum number of colors needed to color the edges of $G$ such that every isomorphic copy of $H$ has at least $q$ colors. In this note, we improve the upper and lower bounds on $r(K_{n, n}, C_{2k}, 3)$. Our upper bound answers a question of Lane and Morrison. For $k=3$ we obtain the asymptotically sharp estimate $r(K_{n, n}, C_6, 3) = \frac{7}{20} n + o(n)$. |
| title | Edge-coloring $K_{n, n}$ with no 2-colored $C_{2k}$ |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2507.13329 |