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2006

Hall ratio of the Mycielski graphs

13 years 11 months ago
Hall ratio of the Mycielski graphs
Let n(G) denote the number of vertices of a graph G and let (G) be the independence number of G, the maximum number of pairwise nonadjacent vertices of G. The Hall ratio of a graph G is defined by (G) = max n(H) (H) : H G , where the maximum is taken over all induced subgraphs H of G. It is obvious that every graph G satisfies (G) (G) (G) where and denote the clique number and the chromatic number of G, respectively. We show that the interval [ (G), (G)] can be arbitrary large by estimating the Hall ratio of the Mycielski graphs.
Mathew Cropper, András Gyárfá
Added 11 Dec 2010
Updated 11 Dec 2010
Type Journal
Year 2006
Where DM
Authors Mathew Cropper, András Gyárfás, Jenö Lehel
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