11 problems

Bollobás–Pebody–Riordan conjecture. For the model with $p(n)=1/2$, the chromatic polynomial is almost complete.

Let $T_{L,L}$ be the diagonal transfer-matrix sub-block for a triangular-lattice strip of width $L$ with fully toroidal boundary conditions, and let $b^{(L)}_1$ denote the stated a…

For a zero-temperature triangular-lattice Potts antiferromagnet on toroidal strips, let $q_0(L)$ and $q_2(L)$ be the relevant real crossings, and let $\ell$ denote the number of br…

Let $q_0(L)$ denote the relevant real crossing for a triangular-lattice strip of width $L$ with fully periodic boundary conditions. Triangular-lattice 3p ± 1 conjecture. For all wi…

For a zero-temperature square-lattice Potts antiferromagnet on toroidal strips, let $q$ be the Potts parameter, let $q_0(L)$ be the relevant real crossing, and let $\ell$ denote th…

Let $q_0(L)$ be the crossing value for an even-width square-lattice strip, with finite-size behavior fitted by $q_0(L)=q_{\rm c}(\mathrm{sq})+A L^{-1/\nu}$. Square-lattice exponent…

Let $q_0(L)$ denote the maximum real value in the limiting curve for a square-lattice strip of width $L$ with fully periodic boundary conditions, and let $q_{\rm c}(\mathrm{sq})=3$…

Let $q_0(L)$ denote the maximum real value in the limiting curve for a square-lattice strip of width $L$ with fully periodic boundary conditions. Odd-width square-lattice conjectur…

JAM's conjecture. The family ${\mathcal G}_{<}(3)$ is enough to establish the existence of a pair of $\chi_{\mathcal P}$-mates for every finite graph property ${\mathcal P}$.

Harary almost-completeness conjecture. There is no Harary polynomial which is almost complete for $\mathbb{G}(n,1/2)$.

Non-completeness conjecture for Harary polynomials. For every non-trivial graph property ${\mathcal P}$, the following forms are conjectured: in the weak form, there exist at least…