Some results on (a:b)-choosability

A solution to a problem of Erdos, Rubin and Taylor is obtained by showing that if a graph G is (a : b)-choosable, and c/d > a/b, then G is not necessarily (c : d)-choosable. The simplest case of another problem, stated by the same authors, is settled, proving that every 2-choosable graph is also (4 : 2)-choosable. Applying probabilistic methods, an upper bound for the kth choice number of a graph is given. We also prove that a directed graph with maximum outdegree d

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Shai Gutner, Michael Tarsi
• Keywords: 2-choosable Graph, CORR 2008, Education, Simplest Case, Solution