  For given a graph $H$, a graphic sequence $\pi=(d_1,d_2,...,d_n)$ is said to
be potentially
  $H$-graphic if there exists a realization of $\pi$ containing $H$ as a
subgraph. In this paper, we characterize the potentially $H$-graphic sequences
where $H$ denotes 3-regular graph with 6 vertices. In other words, we
characterize the potentially $K_{3,3}$ and $K_6-C_6$-graphic sequences where
$K_{r,r}$ is an $r\times r$ complete bipartite graph. One of these
characterizations implies a theorem due to Yin [25].
