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doi:10.1016/j.aml.2005.05.001 
Copyright © 2005 Published by Elsevier Ltd.
Extension of a list coloring problem
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Received 24 November 2004;
revised 10 May 2005;
accepted 16 May 2005.
Available online 21 September 2005.
Abstract
For a graph H, f(H) is the smallest integer k such that the join of H with an empty graph Ek of order k is not |V(H)|-choosable. It was conjectured that for a triangle-free graph G, , where n=|V(G)| and μ(G) is the cardinality of a maximum matching of graph G [S. Gravier, F. Maffray, B. Mohar, On a list-coloring problem, Discrete Math. 268 (2003) 303–308]. We verify this conjecture in the case of forests, and propose some related problems.
Keywords: List coloring; List assignment; Choice number
