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Degree-equipartite graphs

A graph $G$ of order $2n$ is called degree-equipartite if for every $n$-element set $A\subseteq V(G)$, the degree sequences of the induced subgraphs $G[A]$ and $G[V(G)\setminus A]$ are the same. In this paper, we characterize all degree-equipartite graphs. This answers Problem 1 in the paper by Grünbaum et al [B. Grünbaum, T. Kaiser, D. Král, and M. Rosenfeld, Equipartite graphs, {\it Israel J. Math.} {\bf 168} (2008), 431-444].