  Motivated by a possible connection between the $\mathrm{SU}(N)$ instanton
knot Floer homology of Kronheimer and Mrowka and $\mathfrak{sl}(N)$
Khovanov-Rozansky homology, Lobb and Zentner recently introduced a moduli
problem associated to colourings of trivalent graphs of the kind considered by
Murakami, Ohtsuki and Yamada in their state-sum interpretation of the quantum
$\mathfrak{sl}(N)$ knot polynomial. For graphs with two colours, they showed
this moduli space can be thought of as a representation variety, and that its
Euler characteristic is equal to the $\mathfrak{sl}(N)$ polynomial of the graph
evaluated at 1. We extend their results to graphs with arbitrary colourings by
irreducible anti-symmetric representations of $\mathfrak{sl}(N)$.
