Saved in:
| Main Authors: | , , , , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.04055 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- We say a graph $H$ is $r$-rainbow-uncommon if the maximum number of rainbow copies of $H$ under an $r$-coloring of $E(K_n)$ is asymptotically (as $n \to \infty$) greater than what is expected from uniformly random $r$-colorings. Via explicit constructions, we show that for $H\in\{K_3,K_4, K_5\}$, $H$ is $r$-rainbow-uncommon for all $r\geq {|V(H)|\choose 2}$. We also construct colorings to show that for $t \geq 6$, $K_t$ is $r$-rainbow-uncommon for sufficiently large $r$.