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Fan [G. Fan, Distribution of cycle lengths in graphs, J. Combin. Theory Ser. B 84 (2002) 187 -202] proved that if G is a graph with minimum degree δ(G) ≥ 3k for any positive integer k, then G contains k + 1 cycles C 0 , C 1 , .doi:10.1016/j.disc.2008.01.017 fatcat:fhzjeowqu5gorpvvlbjce6sfle