On embedding degree sequences

Assume that we are given two graphic sequences, ${\pi }_1$ and ${\pi }_2$. We consider conditions for ${\pi }_1$ and ${\pi }_2$ which guarantee that there exists a simple graph $G_2$ realizing ${\pi }_2$ such that $G_2$ is the subgraph of any simple graph $G_1$ that realizes ${\pi }_1$.