BibTeX
@MISC{Král03coloringpowers,
author = {Daniel Král},
title = {Coloring Powers of Chordal Graphs},
year = {2003}
}
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Abstract
We prove that the k-th power G of a chordal graph G with maximum degree is O( )-degenerated for even values of k and O( )-degenerated for odd ones. In particular, this bounds the chromatic number (G ). The bound proven for odd values of k is the best possible. Another consequence is the bound (2q 1) + (2p 1) on the least possible span p;q (G) of an L(p; q)-labeling for chordal graphs G with maximum degree . On the other hand, a construction of such graphs with q +p) is presented.
