PLANE EMBEDDING PROBLEMS AND A THEOREM FOR INFINITE MAXIMAL PLANAR GRAPHS

In the first part of this paper we investigate several statements concerning infinite maximal planar graphs which are equivalent in finite case. In the second one, for a given induced $\theta$-path (a finite induced path whose endvertices are adjacent to a vertex of infinite degree) in a 4-connected VAP-free maximal planar graph containing a vertex of infinite degree, a new $\theta$-path is constructed such that the resulting fan is tight.