Abstract: According to a construction of Treumann-Zaslow, a trivalent planar graph in S2 defines a Legendrian surface Σ (a 2:1 branched cover of Sigma) inside the contact manifold J1(S2). In my joint work with Casals and Sackel, we compute the Legendrian contact homology of these, giving a type of "non-abelian" DG expansion of chromatic polynomials. Guided by Nadler-Zaslow "augmentations are sheaves" type conjectures (a sort of "halfway" point of mirror symmetry), this perspective derives previously unknown formulas for the classical chromatic polynomial. Sackel later expanded this algebra to coefficient systems over π1(Σ), in effect relating "Grassmannian transversal colourings" to higher-rank representations of Chekanov-Eliashberg DG algebras.