An Affine Linear Solution for the 2-Face Colorable Gauss Code Problem in the Klein Bottle and a Quadratic System for Arbitrary Closed Surfaces

Sostenes Lins, Emerson Oliveira-Lima, Valdenberg Silva

Let $\bar{P}$ be a sequence of length $2n$ in which each element of $\{1,2,...,n\}$ occurs twice. Let $P^{\prime }$ be a closed curve in a closed surface $S$ having $n$ points of simple aut…