Degree-equipartite graphs

A graph G of order 2 n is called degree-equipartite if for every n -element set A ⊆ V ( G ) , the degree sequences of the induced subgraphs G [ A ] and 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].