2 problems

Let $G$ be a connected non-oriented graph with even $h_G$, and let the low degree of its color factor be the smallest exponent of $N$ with nonzero coefficient. Odd low-degree conje…

Let $G$ be a non-oriented vacuum graph with $v_G\geq4$, and let its color factor be a polynomial or Laurent polynomial in $N$ whose low degree is the smallest exponent of $N$ with…