J.-H. Yin, Department of Mathematics, College of Information Science and Technology, Hainan University, Haikou 570228, P. R. China, e-mail: yinjh@ustc.edu
Abstract: Let $r\ge3$, $n\ge r$ and $\pi=(d_1,d_2,\ldots,d_n)$ be a non-increasing sequence of nonnegative integers. If $\pi$ has a realization $G$ with vertex set $V(G)=\{v_1,v_2,\ldots,v_n\}$ such that $d_G(v_i)=d_i$ for $i=1,2,\ldots, n$ and $v_1v_2\cdots v_rv_1$ is a cycle of length $r$ in $G$, then $\pi$ is said to be potentially $C_r"$-graphic. In this paper, we give a characterization for $\pi$ to be potentially $C_r"$-graphic.
Keywords: graph, degree sequence, potentially $C_r$-graphic sequence
Classification (MSC 2000): 05C07
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