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Gao, Huo, Liu and Ma (2019) proved a result on the existence of pathsconnecting specified two vertices whose lengths differ by one or two. By usingthis result, they settled two famous conjectures due to Thomassen (1983). Inthis paper, we improve their result, and obtain a generalization of a result ofBondy and Vince (1998).

Minimum degree conditions for the existence of a sequence of cycles whose lengths differ by one or two