On Preemptive Resource Constrained Scheduling: Polynomial-Time Approximation Schemes
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
Fractional Path Coloring with Applications to WDM Networks
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Theoretical Computer Science
Coloring fuzzy circular interval graphs
European Journal of Combinatorics
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Let G = (V, E) be a graph and let k be anonnegative integer. A vector c ε ℤV+ is called k-colorable iffthere exists a coloring of G with k colors thatassigns exactly c(v) colors to vertex vε V. Denote by χ (G) andχf(G) the chromatic number andfractional chromatic number, respectively. We prove thatχ(G) = χf(G) holds forevery proper circular arc graph G. For this purpose, a moregeneral round-up property is characterized by means of a polyhedraldescription of all k-colorable vectors. Both round-upproperties are equivalent for proper circular arc graphs. Thepolyhedral description is established and, as a by-product, a knowncoloring algorithm is generalized to multicolorings. The round-upproperties do not hold for the larger classes of circular arcgraphs and circle graphs, unless P = NP. © 2000John Wiley & Sons, Inc. J Graph Theory 33: 256267, 2000