ИСТИНА

Each virtualknot diagramcan be considered asa 4-valent graph where classical crossings play the roleof vertices of the graph andvirtual crossings are just intersection points of images of different edges. Having a 4-valent graph we can construct an Euler tour on it, and the chord diagram and the intersection graph corresponding to the Euler tour. Any two virtual diagrams of the same knot are related to each other by theReidemeister moves. We canextend these moves on intersection graphs. Thisextension depends onthe choice of Euler tours on virtual diagrams. In the talk weconsider two special cases of Euler tours: Gauss circuits and rotating circuits. Weextend the movesto these two cases and construct two new objects: equivalent classes of graphs. We show that these two approaches are equivalent by giving an explicit formula.It is worth to note that we lose some information about a knot when we consider its intersection graph. But some invariants of knots can bedescribed out of intersection graphs.