This paper studies circular chromatic numbers and fractional chromatic numbers of distance graphs G(Z , D) for various distance sets D. In particular, we determine these numbers for those D sets of size two, for some special D sets of size three, for
Fractional chromatic numbers of cones over graphs
β Scribed by Claude Tardif
- Publisher
- John Wiley and Sons
- Year
- 2001
- Tongue
- English
- Weight
- 95 KB
- Volume
- 38
- Category
- Article
- ISSN
- 0364-9024
- DOI
- 10.1002/jgt.1025
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β¦ Synopsis
Abstract
We introduce a construction called the cone over a graph. It is a natural generalisation of Mycielski's construction. We give a formula for the fractional chromatic numbers of all cones over graphs, which generalizes that given in 3 for Mycielski's construction. Β© 2001 John Wiley & Sons, Inc. J Graph Theory 38: 87β94, 2001
π SIMILAR VOLUMES
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The most familiar construction of graphs whose clique number is much smaller than their chromatic number is due to Mycielski, who constructed a sequence G, of triangle-free graphs with ,y(G,) = n. In this article, w e calculate the fractional chromatic number of G, and show that this sequence of num
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## Abstract An Erratum has been published for this article in Journal of Graph Theory 48: 329β330, 2005. Let __M__ be a set of positive integers. The distance graph generated by __M__, denoted by __G__(__Z, M__), has the set __Z__ of all integers as the vertex set, and edges __ij__ whenever |__i__