Geodesic
A note on packing chromatic number of the square lattice
The electronic journal of combinatorics, Tome 17 (2010)
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The concept of a packing colouring is related to a frequency assignment problem. The packing chromatic number $\chi_p(G)$ of a graph $G$ is the smallest integer $k$ such that the vertex set $V (G)$ can be partitioned into disjoint classes $X_1, \dots, X_k$, where vertices in $X_i$ have pairwise distance greater than $i$. In this note we improve the upper bound on the packing chromatic number of the square lattice.
DOI : 10.37236/466
Classification : 05C12, 05C15
Mots-clés : packing chromatic number, packing colouring, square lattice 
@article{10_37236_466,
     author = {Roman Soukal and P\v{r}emysl Holub},
     title = {A note on packing chromatic number of the square lattice},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/466},
     zbl = {1215.05050},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/466/}
}
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Roman Soukal; Přemysl Holub. A note on packing chromatic number of the square lattice. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/466

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