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Group Connectivity and Matchings

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Abstract

Let \(\alpha ^\prime (G)\) be the maximum number of independent edges in a graph \(G\) and \(A\) an abelian group with \(|A|\ge 4\). If a graph \(G^*\) is obtained by repeatedly contracting nontrivial \(A\)-connected subgraphs of \(G\) until no such a subgraph left, then we say \(G\) can be \(A\)-reduced to \(G^*\). In this paper, we show that if \(G\) is a 3-edge-connected simple graph and \(\alpha ^\prime (G)\le 5\), then either \(G\) is \(A\)-connected or \(G\) can be \(A\)-reduced to the Petersen graph.

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Authors and Affiliations

  1. Department of Mathematics, Huazhong Normal University, Wuhan, 430079, China

    Mingfang Huang & Xiangwen Li

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  1. Mingfang Huang
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  2. Xiangwen Li
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Correspondence to Xiangwen Li.

Additional information

M. Huang was supported by the Fundamental Research Funds (WUT: 2013-la-009). X. Li was supported by the Science Foundation of China (11171129) and by Doctoral Fund of Ministry of Education of China (20130144110001).

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Huang, M., Li, X. Group Connectivity and Matchings. Graphs and Combinatorics 31, 993–1001 (2015). https://doi.org/10.1007/s00373-014-1432-2

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  • DOI: https://doi.org/10.1007/s00373-014-1432-2

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