All \(M_{2}\) -Equicoverable Graphs

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• 作者：Yuqin Zhang ; Fan Wu ; Liandi Zhang
• 关键词：H ; covering ; H ; coverable ; H ; equicoverable ; matching
• 刊名：Graphs and Combinatorics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：33
• 期：1
• 页码：245-256
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Combinatorics; Engineering Design;
• 出版者：Springer Japan
• ISSN：1435-5914
• 卷排序：33

文摘

A graph G is called H-equicoverable if every minimal H-covering in G is also a minimum H-covering in G. All \(P_{3}\)-equicoverable graphs were characterized in Zhang (Discret Appl Math 156:647–661, 2008). In 2011, connected \(M_2\)-equicoverable graphs that contains cycles were characterized [see Zhang and Jiang (J Tianjin Univ:44:466–470, 2011) and Zhang and Zhang (Ars Comb 101:45–63, 2011)]. In this paper, we give the characterization of all disconnected \(M_{2}\)-equicoverable graphs and all \(M_{2}\)-equicoverable trees. So all \(M_2\)-equicoverable graphs are characterized now.