A sufficient condition for a plane graph with maximum degree 6 to be class 1
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| Title: | A sufficient condition for a plane graph with maximum degree 6 to be class 1 |
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| Authors: | Wang, Yingqian yqwang@zjnu.cn, Xu, Lingji |
| Source: | Discrete Applied Mathematics. Jan2013, Vol. 161 Issue 1/2, p307-310. 4p. |
| Subjects: | Graph theory, Topological degree, Logical prediction, Graph coloring, Combinatorics, Mathematical analysis |
| Abstract: | Abstract: A well-known conjecture of Vizing (the planar graph conjecture) states that every plane graph with maximum degree is edge -colorable. Vizing himself showed that every plane graph with maximum degree is edge -colorable. Zhang [L. Zhang, Every graph with maximum degree 7 is of class 1, Graphs Combin. 16 (2000) 467–495] and Sanders and Zhao [D. P. Sanders, Y. Zhao, Planar graphs of maximum degree seven are class 1, J. Combin. Theory Ser. B 83 (2001) 201–212] independently proved that every plane graph with maximum degree 7 is of class 1, i.e., edge 7-colorable. This note shows that every plane graph with maximum degree 6 is edge 6-colorable if no vertex in is incident with four faces of size 3. [Copyright &y& Elsevier] |
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| Database: | Engineering Source |
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