The fractional chromatic number of triangle-free graphs with
β Scribed by Linyuan Lu; Xing Peng
- Book ID
- 118735024
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 498 KB
- Volume
- 312
- Category
- Article
- ISSN
- 0012-365X
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π SIMILAR VOLUMES
It follows from the results of , Gyirfis and Lehel (1985), and Kostochka (1988) that 4 ~x\* ## ~5 where x\* = max {X(G): G is a triangle-free circle graph}. We show that X\* ? 5 and thus X\* = 5. This disproves the conjecture of Karapetyan that X\* = 4 and answers negatively a question of Gyirfis
## 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