| 最大度是4的可平面图的边染色 |
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| 引用本文： | 倪伟平.最大度是4的可平面图的边染色[J].枣庄师专学报,2010(5):49-54. |
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| 作者姓名： | 倪伟平 |
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| 作者单位： | 枣庄学院数学与信息科学系,山东枣庄277160 |
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| 摘 要： | 对于最大度是Δ的可平面图G,如果χ′（G）=Δ称G为第一类图,如果χ′（G）=Δ＋1称G为第二类图,χ′（G）表示G的边染色数.1965年,Vizing举例说明,最大度是4的平面图中不仅有第一类图,也有第二类图.论文运用Discharge方法及临界图的重要性质证明：最大度是4,不含5圈和6圈,且任意两个相交面的度不相同的可平面图是第一类图.
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| 关 键 词： | 平面图 边染色 最大度 第一类图 |
Edge Coloring Of Planar Graphs With Δ=4 |
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| NI Wei-ping.Edge Coloring Of Planar Graphs With Δ=4[J].Journal of Zaozhuang Teachers' College,2010(5):49-54. |
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| Authors: | NI Wei-ping |
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| Institution: | NI Wei-ping (Department of Mathematics,Zaozhuang University,Zaozhuang 277160,china) |
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| Abstract: | LetGbe a planar graph of maximum degreeΔ,Gis of class1 ifχ′（G）=Δand of class2 ifχ′（G）=Δ＋1,whereχ′（G） denotes the chromatic index ofG.In 1965,Vizing proved both class 1 and class 2 planar graph exist in planar graphs with Δ=4.By applying a discharging method,we show that a planar graphGwith maximum degree4 is of class 1,ifGdoes not contain 5-cycles and 6-cycles,and contains no intersecting faces with same degrees. |
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| Keywords: | planar graph edge coloring maximum degree class 1 |
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