Edge-(k, l)-Choosability of Planar Graphs without 4-Cycles

Aiming at the conjecture of Erdos, Rubin and Taylor for (k, l)-choosability, in this paper we show that if a planar graph G without 4-cycles and Delta(G) not equal 4, then G is edge-((Delta(G) + 1)m, m)-choosable for all m >= 1, which extend the result that if a planar graph G without 4-cycles, then G is edge- (Delta(G)+1)-choosable [W.F. Wang, Edge choosability of planar graphs without short cycles, Science in China Ser. A, Mathematics, 48 (11) (2005) 1531-1544, and Y Shen et al., Structural properties and edge choosability of planar graphs without 4-cycles, Discrete Mathematics, 308 (23) 2008 5789-5794] in some way.