Degree sequences of graphs containing a cycle with prescribed length
Jian-Hua Yin · Czechoslovak Mathematical Journal · 2009
Let r ≥ 3, n ≥ r and π = (d 1, d 2, ..., d n ) be a non-increasing sequence of nonnegative integers. If π has a realization G with vertex set V (G) = {v 1, v 2, ..., v n } such that d G (v i ) = d i for i = 1, 2, ..., n and v 1 v 2 ... v r v 1 is a cycle of length r in G, then π is said to be potentially C r ″-graphic. In this paper, we give a characterization for π to be potentially C r ″-graphic.