line-equation id-i-eq1"> \(Z_3\) -Connectivity of Claw-Free Graphs

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• 作者：Ziwen Huang ; Xiangwen Li ; Jianqing Ma
• 关键词：Nowhere ; zero k ; flow ; \(Z_3\) ; connectivity ; Claw ; free graph ; Neighborhood intersection
• 刊名：Graphs and Combinatorics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：33
• 期：1
• 页码：123-140
• 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

Jaeger et al. conjectured that every 5-edge-connected graph is \(Z_3\)-connected, which is equivalent to that every 5-edge-connected claw-free graph is \(Z_3\)-connected by Lai et al. (Inf Process Lett 111:1085–1088, 2011), and Ma and Li (Discret Math 336:57–68, 2014). Let G be a claw-free graph on at least 3 vertices such that there are at least two common neighbors of every pair of 2-distant vertices. In this paper, we prove that G is not \(Z_3\)-connected if and only if G is one of seven specified graphs, or three families of well characterized graphs. As a corollary, G does not admit a nowhere-zero 3-flow if and only if G is one of three specified graphs or a family of well characterized graphs.