A note on the minimum number of choosability of planar graphs |
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| Authors: | Huijuan Wang Lidong Wu Xin Zhang Weili Wu Bin Liu |
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| Affiliation: | 1.College of Mathematics,Qingdao University,Qingdao,China;2.Department of Computer Science,University of Texas at Tyler,Tyler,USA;3.School of Mathematics and Statistics,Xidian University,Xi’an,China;4.College of Computer Science and Technology,Taiyuan University of Technology,Taiyuan,China;5.Department of Computer Science,University of Texas at Dallas,Richardson,USA;6.Department of Mathematics,Ocean University of China,Qingdao,China |
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| Abstract: | The problem of minimum number of choosability of graphs was first introduced by Vizing. It appears in some practical problems when concerning frequency assignment. In this paper, we study two important list coloring, list edge coloring and list total coloring. We prove that (chi '_{l}(G)=varDelta ) and (chi ''_{l}(G)=varDelta +1) for planar graphs with (varDelta ge 8) and without adjacent 4-cycles. |
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