On a Conjecture Concerning the Roots of Ehrhart Polynomials of Symmetric Edge Polytopes from Complete Multipartite Graphs

In [7], Higashitani, Kummer, and Michałek pose a conjecture about the symmetric edge polytopes of complete multipartite graphs and confirm it for a number of families in the bipartite case. We confirm that conjecture for a number of new classes following the authors’ methods and we present a more general result which suggests that the methods in their current form might not be enough to prove the conjecture in full generality.