| 若干圈限制平面图的星边染色 |
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| 引用本文： | 谢金苹,徐常青.若干圈限制平面图的星边染色[J].数学进展,2021(2):177-183. |
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| 作者姓名： | 谢金苹 徐常青 |
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| 作者单位： | 河北工业大学理学院 |
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| 基金项目： | 国家自然科学基金(No.11671232)。 |
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| 摘 要： | 图G的星边染色是指G的一个正常边染色,使得G中任一长为4的路和长为4的圈均不是2-边染色的.图G的星边色数χ’st(G)表示图G有星边染色的最小颜色数.设G是最大度为Δ的平面图,我们证明了:(1)若G不含4-圈,则χ’st(G)≤1.5Δ]+15;(2)若g≥5,则χ’st(G)≤1.5Δ」+10;(3)若g=7,则χ’st(G)≤1.5Δ」+6.
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| 关 键 词： | 平面图 星边染色 星边色数 |
Star Edge-colorings of Plane Graphs with Cycle Conditions |
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| XIE Jinping,XU Changqing.Star Edge-colorings of Plane Graphs with Cycle Conditions[J].Advances in Mathematics,2021(2):177-183. |
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| Authors: | XIE Jinping XU Changqing |
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| Institution: | (School of Science,Hebei University of Technology,Tianjin,300401,P.R.China) |
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| Abstract: | A star edge-coloring of a graph G is a proper edge coloring without 2-colored paths or cycles of length 4.The smallest number for which G admits a star edge-coloring is called the star chromatic index,denoted by χ’st(G).Let G be a plane graph with maximum degree Δ.We prove that:(1) If G contains no 4-cycles,then χ’st ≤ 1.5Δ]+ 15;(2) If g≥ 5,then χ’st(G)≤1.5Δ]+ 10;(3) If g=7,then χ’st(G) ≤1.5Δ]+6. |
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| Keywords: | plane graph star edge-coloring star chromatic index |
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