English

Abstract:
Conway and Gordon showed that every embedding of the complete graph on seven vertices into the 3-space contains a nontrivial knot. On the other hand Kinoshita showed that for any $n(n-1)/2$ knot types there is an embedding of the $\theta_n$-curve into the 3-space that realizes the knot types at once. These results exhibit restrictions and possibilities of realizing knot types in a spatial graph at once. In this talk we will give a survey on this topic and related topics.