ИСТИНА

V.A. Vassiliev in his paper on finite type invariants of self-intersecting curves, V.A. Vassiliev conjectured a criterion of planarity of framed four-valent graphs, i.e. 4-graphs with an opposite edge structure at each vertex. The conjecture was proved by V.O. Manturov, who used the d-diagram technics he developed. We give here another proof of Vassiliev's planarity criterion of framed four-valent graphs (and more generally, (even) star-graphs), which is based on Pontryagin-Kuratowski theorem.