## 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 &
The fractional matching numbers of graphs
β Scribed by Yan Liu; Guizhen Liu
- Publisher
- John Wiley and Sons
- Year
- 2002
- Tongue
- English
- Weight
- 85 KB
- Volume
- 40
- Category
- Article
- ISSN
- 0028-3045
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
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
## Abstract The fractional chromatic number of a graph __G__ is the infimum of the total weight that can be assigned to the independent sets of __G__ in such a way that, for each vertex __v__ of __G__, the sum of the weights of the independent sets containing __v__ is at least 1. In this note we g
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
## Abstract In 1959, even before the FourβColor Theorem was proved, GrΓΆtzsch showed that planar graphs with girth at least 4 have chromatic number at the most 3. We examine the fractional analogue of this theorem and its generalizations. For any fixed girth, we ask for the largest possible fraction