Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.16573 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- For a non-decreasing sequence of positive integers $S = (a_1, a_2,\ldots)$, the $S$-packing chromatic number of a graph $G$ is the smallest positive integer $k$ such that the vertices can be colored with $k$ colors, where the distance between any two distinct vertices of color $i$ is greater than $a_i$. In this paper, we show that the $S$-packing chromatic number of the infinite diagonal grid $P_\infty \boxtimes P_\infty$ with $S = (1,6,6,\ldots)$ is $40$. This confirms a conjecture of the first author and Tiyajamorn.