Nonnegativity of the gamma-polynomial of symmetric edge polytopes

Prove that the gamma-polynomial associated with the h*-polynomial of the symmetric edge polytope of every graph has nonnegative coefficients.

Background

The paper studies symmetric edge polytopes P_G and their Ehrhart-theoretic h*-polynomials. Because these h*-polynomials are palindromic, they can be expressed in the gamma-basis, producing a gamma-polynomial gamma_{P_G}(t). The conjecture attributed to Ohsugi and Tsuchiya asserts coefficientwise nonnegativity of this polynomial for every graph.

The authors explain that the conjecture had previously been verified only for special graph families or for the first few gamma-coefficients. Establishing it would give a strong form of positivity for the h*-polynomials of symmetric edge polytopes.