Gamma-nonnegative edge deletion for some edge

Determine, for every 2-connected graph G, an edge e such that the difference h*_{P_G}(t)-h*_{P_{G\setminus e}}(t) is gamma-nonnegative.

Background

The authors seek an inductive proof of gamma-positivity for the h*-polynomial of every symmetric edge polytope. Such an induction would follow if, in every 2-connected graph, one could delete an edge while preserving gamma-nonnegativity of the resulting difference.

The paper proves that an appropriate edge always exists for the quadratic gamma-coefficient, but it does not establish the full gamma-nonnegativity required by this conjecture.

References

Let $G$ be a 2-connected graph. There exists an edge $e \in E$ such that $h*_{P_G}(t) - h*{P{G e}(t)$ is $\gamma$-nonnegative.

— The number of edges of a symmetric edge polytope  (2512.16572 - Codenotti et al., 18 Dec 2025) in Conjecture 3.1, Section 3 (Connection to the Ehrhart theory of symmetric edge polytopes)