6 problems

Let $G$ be a graph of order $n$, let $\overline{G}$ be its complement, and let $\gamma(G)$ denote the genus of $G$. For $n\geq 11$, consider the lower bound … for…

Let $G$ be a cyclic group whose order has three distinct prime factors, and let $\Gamma(G)$ denote its subgroup lattice graph. Proposition upper bounds the genus…

A cubic graph is a graph in which every vertex has degree three. Mohar's conjecture. Approximating the genus of cubic graphs is APX-hard. This conjecture asserts computational hard…

Ringel's conjecture. For the missing cases $n\equiv 5,9\pmod{12}$, this lower bound is attained except when $n=5$; that is, for these cases with $n\ne5$,

Let $(G,\rho)$ be a ribbon graph. Write $V(G)$ for its vertices, $E(G)$ for its edges, $\operatorname{Pic}^0(G)$ for its degree-zero Picard group, and $\mathcal{T}(G)\subset E(G)$…

Clarke-Fiorini-Joret-Theis conjecture. For every positive integer $g$,