We prove that every 3-chromatic claw-free perfect graph is 3-choosable.
On the Lucky Choice Number of Graphs
β Scribed by S. Akbari, M. Ghanbari, R. Manaviyat, S. Zare
- Book ID
- 120788665
- Publisher
- Springer Japan
- Year
- 2011
- Tongue
- English
- Weight
- 151 KB
- Volume
- 29
- Category
- Article
- ISSN
- 0911-0119
No coin nor oath required. For personal study only.
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We show that the choice number of a graph G is equal to its chromatic number when G belongs to a restricted class of claw-free graphs, in view of the conjecture that this is true for every claw-free graph. We consider only finite, undirected graphs, without loops. Given a graph G = ( V, E), a k-col
## Abstract We calculate the asymptotic value of the choice number of complete multiβpartite graphs, given certain limitations on the relation between the sizes of the different sides. In the bipartite case, we prove that if __n__~0~ β€ __n__~1~ and log__n__~0~ β« loglog__n__~1~, then $ch(K\_{n\_{0},