The packing coloring of distance graphs D(k, t)

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F14%3A43921448" target="_blank" >RIV/49777513:23520/14:43921448 - isvavai.cz</a>
Result on the web
<a href="http://www.sciencedirect.com/science/article/pii/S0166218X13004794" target="_blank" >http://www.sciencedirect.com/science/article/pii/S0166218X13004794</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.dam.2013.10.036" target="_blank" >10.1016/j.dam.2013.10.036</a>

Result language
angličtina
Original language name
The packing coloring of distance graphs D(k, t)
Original language description
The packing chromatic number $chi_{rho}(G)$ of a graph $G$ is the smallest integer $p$ such that vertices of $G$ can be partitioned into disjoint classes $X_{1}, ..., X_{p}$ where vertices in $X_{i}$ have pairwise distance greater than $i$. For $k { t$we study the packing chromatic number of infinite distance graphs $D(k, t)$, i.e. graphs with the set $Z$ of integers as vertex set and in which two distinct vertices $i, j in Z$ are adjacent if and only if $|i - j| in {k, t}$. We generalize results by Ekstein et al. for graphs $D (1, t)$. For sufficiently large $t$ we prove that $chi_{rho}(D(k, t)) leq 30$ for both $k$, $t$ odd, and that $chi_{rho}(D(k, t)) leq 56$ for exactly one of $k$, $t$ odd. We also give some upper and lower bounds for $chi_{rho}(D(k, t))$ with small $k$ and $t$.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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