Corpus ID: 218763281

# $S$-packing colorings of distance graphs $G(\mathbb{Z},\{2,t\})$

@article{Brevsar2020SpackingCO,
title={\$S\$-packing colorings of distance graphs \$G(\mathbb\{Z\},\\{2,t\\})\$},
author={Bovstjan Brevsar and Jasmina Ferme and Karol'ina Kamenick'a},
journal={arXiv: Combinatorics},
year={2020}
}
• Published 2020
• Mathematics
• arXiv: Combinatorics
• Given a graph $G$ and a non-decreasing sequence $S=(a_1,a_2,\ldots)$ of positive integers, the mapping $f:V(G) \rightarrow \{1,\ldots,k\}$ is an $S$-packing $k$-coloring of $G$ if for any distinct vertices $u,v\in V(G)$ with $f(u)=f(v)=i$ the distance between $u$ and $v$ in $G$ is greater than $a_i$. The smallest $k$ such that $G$ has an $S$-packing $k$-coloring is the $S$-packing chromatic number, $\chi_S(G)$, of $G$. In this paper, we consider the distance graphs $G(\mathbb{Z},\{2,t… CONTINUE READING #### Figures from this paper. #### References ##### Publications referenced by this paper. SHOWING 1-10 OF 22 REFERENCES ## Packing$(1,1,2,2)$-coloring of some subcubic graphs. • Mathematics • 2019 ## Packing chromatic number,$(1,1,2,2)\$-colorings, and characterizing the Petersen graph

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