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  • On the packing chromatic number of square and hexagonal lattice
    Korže, Danilo ; Vesel, Aleksander
    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▫ $X_1, \dots , X_k$▫, with the ... condition that vertices in ▫$X_i$▫ have pairwise distance greater than ▫$i$▫. We show that the packing chromatic number for the hexagonal lattice ▫$\mathcal{H}$▫ is 7. We also investigate the packing chromatic number for infinite subgraphs of the square lattice ▫$\mathbb{Z}^2$▫ with up to 13 rows. In particular, we establish the packing chromatic number for ▫$P_6 \Box \mathbb{Z}$▫ and provide new upper bounds on these numbers for the other subgraphs of interest. Finally, we explore the packing chromatic number for some infinite subgraphs of ▫$\mathbb{Z}^2 \Box P_2$▫. The results are partially obtained by a computer search.
    Vir: Ars mathematica contemporanea. - ISSN 1855-3966 (Vol. 7, no. 1, 2014, str. 13-22)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2014
    Jezik - angleški
    COBISS.SI-ID - 17063446

    Povezava(-e):

    http://amc-journal.eu/index.php/amc/article/view/255/224
    Digitalna knjižnica Univerze v Mariboru – DKUM
    Digitalna knjižnica Slovenije - dLib.si
    DOI

vir: Ars mathematica contemporanea. - ISSN 1855-3966 (Vol. 7, no. 1, 2014, str. 13-22)

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