When is ch(K(m,n))=m-1?
Nurit Gazit
Abstract
Let nm be the smallest integer n such that ch(Km,n) = m-1, where ch(G) denotes the choice (list chromatic) number of the graph G. We prove that there is an infinite sequence of integers S, such that if m is in S, then nm <= 0.4643 ((m-2)(m-2)). If m -> infinity, then nm is asymptotically at most 0.474 ((m-2)(m-2)).
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