On the topology of planar real decomposable curves of degree 8

We consider the problem of topological classification of arrangements in the real projective plane of the union of nonsingular curves of degrees $2$ and $6$ under certain conditions of maximality and general position. We list admissible topological models of such arrangements to be studied by using the Orevkov method based on the theory of braids and links and prove that most of these models cannot be realized by curves of degree $8$.