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Vertex coloring inherited from perfect matchings (motivated by quantum physics)
Added (19.01.2021): Dustin Mixon wrote a blog post about the question where he reformulated and generalized the question.
Added (25.12.2020): I made a youtube video to explain the question in detail.
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Does Ising partition function determine the number of $k$-matchings mod $4$ for cubic graphs?
Let $G$ be a cubic graph. It's known that the Tutte polynomial $T_G$ of $G$ on the hyperbola $(x-1)(y-1)=2$ determines the Ising partition function of $G$ and vice versa.
A $k$-matching in a graph $G$ ...
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