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Jaeger et al. conjectured that every 5-edge-connected graph is Z_3-connected.  In this paper, we prove that every 4-edge-connected K_{1, 3}-free graph without any induced cycle of length at least 5 is Z_3-connected, which partially generalizes the earlier results of Lai [Graphs and Combin. 16 (2000) 165-176] and Fukunaga [Graphs and Combin. 27 (2011) 647-659].

Z_3-connectivity of K_{1,3}-free graphs without induced cycle of length at least 5