A Dynamic View of Circular Colorings
Combinatorics
2007-05-23 v1 Distributed, Parallel, and Cluster Computing
Discrete Mathematics
Abstract
The main contributions of this paper are three-fold. First, we use a dynamic approach based on Reiter's pioneering work on Karp-Miller computation graphs to give a new and short proof of Mohar's Minty-type Theorem. Second, we bridge circular colorings and discrete event dynamic systems to show that the Barbosa and Gafni's results on circular chromatic number can be generalized to edge-weighted symmetric directed graphs. Third, we use the above-mentioned dynamic view of circular colorings to construct new improved lower bounds on the circular chromatic number of a graph. We show as an example that the circular chromatic number of the line graph of the Petersen graph can be determined very easily by using these bounds.
Cite
@article{arxiv.math/0604226,
title = {A Dynamic View of Circular Colorings},
author = {Hong-Gwa Yeh},
journal= {arXiv preprint arXiv:math/0604226},
year = {2007}
}
Comments
23 pages