科研之友
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摘要
Let G be the graph obtained from K-3,K-3 by deleting an edge. We find a list assignment with vertical bar L(nu)vertical bar = 2 for each vertex nu of G, such that G is uniquely L-colorable, and show that for any list assignment L' of G, if vertical bar L'(nu)vertical bar >= 2 for all nu is an element of V(G) and there exists a vertex nu(0) with vertical bar L'(nu(0))vertical bar > 2, then G is not uniquely L'-colorable. However, G is not 2-choosable. This disproves a conjecture of Akbari, Mirrokni, and Sadjad (Problem 404 in Discrete Math. 266(2003) 441-451).
