Radio k-colorings of paths
Gary Chartrand ; Ladislav Nebeský ; Ping Zhang
Discussiones Mathematicae Graph Theory, Tome 24 (2004), p. 5-21 / Harvested from The Polish Digital Mathematics Library
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For a connected graph G of diameter d and an integer k with 1 ≤ k ≤ d, a radio k-coloring of G is an assignment c of colors (positive integers) to the vertices of G such that d(u,v) + |c(u)- c(v)| ≥ 1 + k for every two distinct vertices u and v of G, where d(u,v) is the distance between u and v. The value rcₖ(c) of a radio k-coloring c of G is the maximum color assigned to a vertex of G. The radio k-chromatic number rcₖ(G) of G is the minimum value of rcₖ(c) taken over all radio k-colorings c of G. In this paper, radio k-colorings of paths are studied. For the path Pₙ of order n ≥ 9 and n odd, a new improved bound for rcn-2(Pₙ) is presented. For n ≥ 4, it is shown that rcn-3(Pₙ)≤n-22 Upper and lower bounds are also presented for rcₖ(Pₙ) in terms of k when 1 ≤ k ≤ n- 1. The upper bound is shown to be sharp when 1 ≤ k ≤ 4 and n is sufficiently large.

Publié le : 2004-01-01
EUDML-ID : urn:eudml:doc:270733 
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Gary Chartrand; Ladislav Nebeský; Ping Zhang. Radio k-colorings of paths. Discussiones Mathematicae Graph Theory, Tome 24 (2004) pp. 5-21. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1209/

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