数学季刊 >

2022 , Vol. 37 >Issue 4: 380 - 385

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2022.04.005

哈林图的导出匹配可扩性

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  • 1. School of Mathematics and Statistics, Pingdingshan University, Pingdingshan 467000, China; 2. International Joint Laboratory for Multidimensional Topology and Carcinogenic Characteristics Analysis of Atmospheric Particulate Matter PM2.5, Pingdingshan 467000, China; 3. School of Software, Pingdingshan University, Pingdingshan 467000, China
ZHANG Qing-nan (2000-), female, native of Kaifeng, Henan, undergraduate students of Pingdingshan University, engages in graph calculation; HUI Zhi-hao (1980-), male, native of Nanyang, Henan, associate professor of Pingdingshan University, engages in graph theory and network optimization; YANG Yu (1983-), male, native of Nanyang, Henan, associate professor of Pingdingshan University, engages in graph computing and big data technology; WANG An (1983-), male, native of Kaifeng, Henan, lecturer of Pingdingshan University, engages in grey systems and machine learning.

收稿日期: 2022-05-20

  网络出版日期: 2022-12-30

基金资助

 Supported by the National Natural Science Foundation of China (Grant Nos. 61702291, 11801371); Key Research Project in Universities of Henan Province (Grant No. 21B110004). 

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Induced Matching-Extendability of Halin Graphs

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  • 1. School of Mathematics and Statistics, Pingdingshan University, Pingdingshan 467000, China; 2. International Joint Laboratory for Multidimensional Topology and Carcinogenic Characteristics Analysis of Atmospheric Particulate Matter PM2.5, Pingdingshan 467000, China; 3. School of Software, Pingdingshan University, Pingdingshan 467000, China
ZHANG Qing-nan (2000-), female, native of Kaifeng, Henan, undergraduate students of Pingdingshan University, engages in graph calculation; HUI Zhi-hao (1980-), male, native of Nanyang, Henan, associate professor of Pingdingshan University, engages in graph theory and network optimization; YANG Yu (1983-), male, native of Nanyang, Henan, associate professor of Pingdingshan University, engages in graph computing and big data technology; WANG An (1983-), male, native of Kaifeng, Henan, lecturer of Pingdingshan University, engages in grey systems and machine learning.

Received date: 2022-05-20

  Online published: 2022-12-30

Supported by

 Supported by the National Natural Science Foundation of China (Grant Nos. 61702291, 11801371); Key Research Project in Universities of Henan Province (Grant No. 21B110004). 

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摘要

 Let G be a connected graph having a perfect matching. The graph G is said to be induced matching (IM) extendable if every induced matching M of G is contained in a perfect matching of G. In this paper, we show that Halin graph G =T ∪C is IMextendable if and only if its characteristic tree T is isomorphic to K1,3, K1,5, K1,7 or S2,2.

关键词： Halin graph; Perfect matching; Induced matching; Induced matching extendable

本文引用格式

张庆楠, 惠志昊, 杨雨, 王安 . 哈林图的导出匹配可扩性[J]. 数学季刊, 2022 , 37(4) : 380 -385 . DOI: 10.13371/j.cnki.chin.q.j.m.2022.04.005

Abstract

 Let G be a connected graph having a perfect matching. The graph G is said to be induced matching (IM) extendable if every induced matching M of G is contained in a perfect matching of G. In this paper, we show that Halin graph G =T ∪C is IMextendable if and only if its characteristic tree T is isomorphic to K1,3, K1,5, K1,7 or S2,2.

Key words： Halin graph; Perfect matching; Induced matching; Induced matching extendable

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