Positivity conjecture for Chern–Schwartz–MacPherson classes of graph hypersurfaces

Let $X_\Gamma=\{\Psi_\Gamma=0\}$ be the graph hypersurface associated with a graph $\Gamma$, embedded in its ambient projective space, and let $H$ denote the hyperplane class. Write its Chern–Schwartz–MacPherson class as a polynomial in powers of $H$. Positivity conjecture. The coefficients of all powers $H^k$ in the Chern–Schwartz–MacPherson class of an arbitrary graph hypersurface $X_\Gamma$ are non-negative. The conjecture proposes a general positivity phenomenon for Chern–Schwartz–MacPherson classes of graph hypersurfaces, motivated by computations for banana graphs and other sample Feynman graphs. At the time of the source, no conceptual explanation or general proof was known.