On Realizability of Gauss Diagrams
  The problem of which Gauss diagram can be realized by knots is an old one and has been solved in several ways. In this paper, we present a direct approach to this problem. We show that the needed conditions for realizability of a Gauss diagram can be interpreted as follows "the number of exits = the number of entrances" and the sufficient condition is based on Jordan curve Theorem. 
Andrey Grinblat and Viktor Lopatkin
math.GT