# Archdeacon, Dan

## Crossing sequences ★★

Author(s): Archdeacon; Bonnington; Siran

\begin{conjecture} Let $(a_0,a_1,a_2,\ldots,0)$ be a sequence of nonnegative integers which strictly decreases until $0$.

Then there exists a graph that be drawn on a surface with orientable (nonorientable, resp.) genus $i$ with $a_i$ crossings, but not with less crossings. \end{conjecture}

Keywords: crossing number; crossing sequence