4 problems

Billera–Lee upper-bound conjecture. For every integer $i$ with $0\leq i\leq d$,

Billera–Lee upper-bound conjecture. The inequality

Let $\hat{G}$ be a block and hole graph with one pentagonal block and two quadrilateral holes, or, two quadrilateral blocks and one pentagonal hole. The 5-connectivity conjecture.…

Let $d$ and $k$ be integers with $d\geq 2k+1$, and let $X$ be a triangulated $d$-sphere with face-vector $(f_0,\dots,f_d)$. Generalized lower bound conjecture. For every $j$, the f…