S. B. Rao's well-quasi-ordering conjecture for degree sequences

Let a graphic degree sequence be a multiset of non-negative integers realized as the degree sequence of a simple graph. For a degree sequence $D$, let

$$\mathcal{R}(D)=\{G\mid D(G)=D\}$$

be its set of realizations. Define $D\preceq D'$ if there exist $G\in\mathcal{R}(D)$ and $G'\in\mathcal{R}(D')$ such that $G$ is an induced subgraph of $G'$. Rao's conjecture. The degree sequences are well-quasi-ordered with respect to the relation $\preceq$. Chudnovsky and Seymour announced a proof of this conjecture, so the claim is no longer open.