1. On the packing coloring of base-3 Sierpiński graphs and H-graphs.
- Author
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Deng, Fei, Shao, Zehui, and Vesel, Aleksander
- Subjects
- *
CHROMATIC polynomial , *GRAPH coloring , *INTEGERS , *COLOR - Abstract
For a nondecreasing sequence of integers S = (s 1 , s 2 , ...) an S-packing k-coloring of a graph G is a mapping from V(G) to { 1 , 2 , ... , k } such that vertices with color i have pairwise distance greater than s i . By setting s i = d + ⌊ i - 1 n ⌋ we obtain a (d, n)-packing coloring of a graph G. The smallest integer k for which there exists a (d, n)-packing coloring of G is called the (d, n)-packing chromatic number of G. In the special case when d and n are both equal to one we obtain the packing chromatic number of G. We determine the packing chromatic number of base-3 Sierpiński graphs and provide new results on (d, n)-packing chromatic colorings for this class of graphs. By using a dynamic algorithm, we establish the packing chromatic number for H-graphs. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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