KMS Of Academy of mathematics and systems sciences, CAS
Improved Upper Bounds on Acyclic Edge Colorings | |
其他题名 | Improved upper bounds on acyclic edge colorings |
Wu Yuwen1; Yan Guiying2 | |
2014-01-01 | |
发表期刊 | ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES |
ISSN | 0168-9673 |
卷号 | 30期号:2页码:305-308 |
摘要 | An acyclic edge coloring of a graph is a proper edge coloring such that every cycle contains edges of at least three distinct colors. The acyclic chromatic index of a graph G, denoted by a'(G), is the minimum number k such that there is an acyclic edge coloring using k colors. It is known that a'(G) <= 16 del for every graph G where del denotes the maximum degree of G. We prove that a'(G) < 13.8 del for an arbitrary graph G. We also reduce the upper bounds of a'(G) to 9.8 del and 9 del with girth 5 and 7, respectively. |
其他摘要 | Abstract(#br)An a cyclic edge coloring of a graph is a proper edge coloring such that every cycle contains edges of at least three distinct colors. The a cyclic chromatic index of a graph G , denoted by a ′( G ), is the minimum number k such that there is an acyclic edge coloring using k colors. It is known that a ′( G ) ≤ 16Δ for every graph G where Δ denotes the maximum degree of G . We prove that a ′( G ) < 13.8Δ for an arbitrary graph G . We also reduce the upper bounds of a ′( G ) to 9.8Δ and 9Δ with girth 5 and 7, respectively. |
关键词 | graph coloring acyclic edge coloring Lovasz local lemma |
收录类别 | CSCD |
语种 | 英语 |
资助项目 | [National Natural Science Foundation of China] |
CSCD记录号 | CSCD:5102536 |
引用统计 | |
文献类型 | 期刊论文 |
条目标识符 | http://ir.amss.ac.cn/handle/2S8OKBNM/54755 |
专题 | 应用数学研究所 |
作者单位 | 1.北京物资学院 2.中国科学院数学与系统科学研究院 |
推荐引用方式 GB/T 7714 | Wu Yuwen,Yan Guiying. Improved Upper Bounds on Acyclic Edge Colorings[J]. ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES,2014,30(2):305-308. |
APA | Wu Yuwen,&Yan Guiying.(2014).Improved Upper Bounds on Acyclic Edge Colorings.ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES,30(2),305-308. |
MLA | Wu Yuwen,et al."Improved Upper Bounds on Acyclic Edge Colorings".ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES 30.2(2014):305-308. |
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