Abstract
Jaeger et al. (J Comb Theory Ser B 56:165–182, 1992) conjectured that every 5-edge-connected graph is \(Z_3\)-connected. Moreover, Lai et al. (Discret Math 311:2295–2307, 2011) proved that every 5-edge-connected graph is \(Z_3\)-connected if and only if every 5-edge-connected line graph is \(Z_3\)-connected. A graph \(G\) is a \(J_3\) graph if every edge of \(G\) lies in a 3-cycle of \(G\). We prove that every 5-edge-connected \(J_3\) line graph is \(Z_3\)-connected.
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Acknowledgments
The authors would like to thank Professor Lai for the valuable comments. The first author was supported by National Science Foundation of China (11326215). The second author was supported by National Science Foundation of China (11171129).
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Yang, F., Li, X. Group connectivity in \(J_3\) line graphs. Graphs and Combinatorics 31, 1065–1076 (2015). https://doi.org/10.1007/s00373-014-1418-0
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DOI: https://doi.org/10.1007/s00373-014-1418-0