236 research outputs found
Notes on complexity of packing coloring
A packing -coloring for some integer of a graph is a mapping
such that any two vertices of color
are in distance at least . This concept
is motivated by frequency assignment problems. The \emph{packing chromatic
number} of is the smallest such that there exists a packing
-coloring of .
Fiala and Golovach showed that determining the packing chromatic number for
chordal graphs is \NP-complete for diameter exactly 5. While the problem is
easy to solve for diameter 2, we show \NP-completeness for any diameter at
least 3. Our reduction also shows that the packing chromatic number is hard to
approximate within for any .
In addition, we design an \FPT algorithm for interval graphs of bounded
diameter. This leads us to exploring the problem of finding a partial coloring
that maximizes the number of colored vertices.Comment: 9 pages, 2 figure
On the r-dynamic coloring of the direct product of a path with either a complete graph or a wheel graph
In this paper, it is explicitly determined the r-dynamic chromatic number of the direct
product of any given path with either a complete graph or a wheel graph. Illustrative examples are
shown for each one of the cases that are studied throughout the paper.Junta de AndalucÃa FQM-01
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