Ehrhart positivity of matching polytopes of finite simple graphs

Prove that the matching polytope of every finite simple graph is Ehrhart positive, so that all coefficients of its Ehrhart polynomial are nonnegative.

Background

The paper proves Ehrhart positivity for matching polytopes of forests and discusses additional positive families, including even cycles and complete bipartite graphs in several cases. These results motivate a conjecture extending positivity to arbitrary finite simple graphs.

The conjecture is not resolved in the paper; it is presented after the established special cases and computational evidence for complete bipartite graphs.

References

Matching polytopes of finite simple graphs are Ehrhart positive.

— Series-parallel extensions and Ehrhart positivity  (2610.03122 - Li et al., 2 Oct 2026) in Section 8, Matching polytopes, immediately following the discussion of forests, even cycles, and complete bipartite graphs; Conjecture 8.1 (labeled conj:matching-ehrhart-positive)