4 problems

Full windmill maximizer conjecture. Among graphs with $n$ vertices and $3(n-1)/2$ edges, for odd $n$, $WM(n)$ is a facet maximizer. More generally, any graph that is a join of…

Coffee-bean maximizer conjecture. The facet count $N(CB(x_1,x_2,x_3))$ is maximized by

Different-parity coffee-bean conjecture. If $x_1$, $x_2$, and $x_3$ have different parities, then

Facet-count bounds conjecture. If $n=2k$ with $k\geq 2$, then $F(x_1,x_2,x_3)$ is maximized at $F(n-1,1,1)$. If $n=2k-1$ with $k\geq 3$, then it is maximized at $F(n-3,2,2)$. Furth…