| 最小1-因子覆盖集的若干结果 |
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| 引用本文： | 翟绍辉,郭晓峰.最小1-因子覆盖集的若干结果[J].数学研究,2008,41(1):24-30. |
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| 作者姓名： | 翟绍辉 郭晓峰 |
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| 作者单位： | 1. 橱建省厦门理工学院数理系,福建,厦门,361024
2. 福建省厦门大学数学科学学院,福建,厦门,361005 |
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| 摘 要： | 假设G是一个1-可扩图．G的1-因子覆盖是G的某些1-因子的集合M使得∪M∈M M=F（G）．1-因子数目最小的1．因子覆盖称为excessive factorization．一个excessive factorization中的1．因子数目称为图G的excessive index，记为x：（G）．本文我们基于G的耳朵分解和E（C）的依赖关系给出了X＇e（G）的上界．对任意正整数k≥3，我们构造出一个图G使得A（G）=3而X＇e（G）=k．进而，我们考虑了乘积图的excessive index．
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| 关 键 词： | 1-可扩图 1-因子覆盖 Excessive index |
| 修稿时间： | 2007年7月8日 |
Some Results of Minimum Sets of 1-Factors Covering a Graph |
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| Zhai Shaohui,Guo Xiaofeng.Some Results of Minimum Sets of 1-Factors Covering a Graph[J].Journal of Mathematical Study,2008,41(1):24-30. |
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| Authors: | Zhai Shaohui Guo Xiaofeng |
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| Institution: | Zhai Shaohui Guo Xiaofeng( 1. Department of Mathematics and Physics, Xiamen University of Technology; Xiamen Fujian 361024; 2. School of Mathematical Sciences, Xiamen University, Xiamen Fujian 361005 ) |
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| Abstract: | Let G be a 1-extendable graph. A 1-factor cover of G is a set Μ of 1-factors of G such that UM∈ΜM=E(G). A 1-factor cover of minimum cardinality is called an excessive factorization. The excessive index of G, denote χ′e(G), is the size of an excessive factorization of G. In the present paper, we obtain a tight upper bound of χ′e(G) based on dependence relation on E(G) and ear decomposition of G. For any positive integer κ≥3, we construct a graph G with△(G) = 3 and χ′e(G) = κ. In addition, we also consider the excessive index of the Cartesian product of two graphs. |
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| Keywords: | 1-extendable graphs 1-factor cover Excessive index |
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