Let r 3, n r and π = (d1, d2, . . . , dn) be a graphic sequence. If there exists a simple graph G on n vertices having degree sequence π such that G contains Cr (a cycle of length r) as a subgraph, then π is said to be potentially Cr-graphic. Li and Yin (2004) posed the following problem: characterize π = (d1, d2, . . . , dn) such that π is potentially Cr-graphic for r 3 and n r. Rao and Rao (1972) and Kundu (1973) answered this problem for the case of n = r. In this paper, this problem is solved completely.
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