Degree-equipartite graphs

A graph GG of order 2n2n is called degree-equipartite if for every nn-element set A⊆V(G)A⊆V(G), the degree sequences of the induced subgraphs G[A]G[A] and G[V(G)∖A]G[V(G)∖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, Israel J. Math. 168 (2008) 431–444].