Facets and facet subgraphs of adjacency polytopes

Adjacency polytopes, a.k.a. symmetric edge polytopes, associated with undirected graphs have been defined and studied in several seemingly-independent areas including number theory, discrete geometry, and dynamical systems. In particular, the authors are motivated by the study of the algebraic Kuramoto equations of unmixed form whose Newton polytopes are the adjacency polytopes. The interplay between the geometric structure of adjacency polytopes and the topological structure of the underlying graphs is a recurring theme in recent studies. In particular, "facet/face subgraphs" emerged as one of the central concepts in describing this symmetry. Continuing along this line of inquiry we provide a complete description of the correspondence between facets/faces of an adjacency polytope and maximal bipartite subgraphs of the underlying connected graph.