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Structural properties and edge choosability of planar graphs without 4-cycles |
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| Authors: | Yufa Shen Guoping Zheng Yongqiang Zhao |
| Affiliation: | a Department of Mathematics and Physics, Hebei Normal University of Science and Technology, Qinhuangdao 066004, PR China b Applied Mathematics Institute, Hebei University of Technology, Tianjin 300130, PR China c Department of Mathematics, Shijiazhuang College, Shijiazhuang 050801, PR China d Center for Mathematics of Hebei Province, Hebei Normal University, Shijiazhuang 050016, PR China |
| Abstract: | Some structural properties of planar graphs without 4-cycles are investigated. By the structural properties, it is proved that every planar graph G without 4-cycles is edge-(Δ(G)+1)-choosable, which perfects the result given by Zhang and Wu: If G is a planar graph without 4-cycles, then G is edge-t-choosable, where t=7 if Δ(G)=5, and otherwise t=Δ(G)+1. |
| Keywords: | Planar graphs Cycles Edge choosability |
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