4-connected Planar Graphs are Inscribable M.B. Dillencourt, University of California;W.D. Smith, NEC 12/10/91 ABSTRACT: This is part of a series of TMs exploring graph-theoretic consequences of the recent Rivin-Smith characterization of ``inscribable graphs.'' The purpose of the present TM is to prove that all ``4-connected planar'' graphs are inscribable. (A graph is a set of ``vertices,'' some pairs of which are joined by ``edges.'' A graph is ``inscribable'' if it is the 1-skeleton of a convex polyhedron inscribed in a sphere. A graph is ``planar'' if it may be drawn in the plane with edges being represented by Jordan curves, and with no edge-crossings. A graph is ``4-connected'' if it cannot be disconnected by the removal of fewer than 4 vertices.) This TM will later be incorporated into a joint publication by Dillencourt and Smith on ``Graph-Theoretic Properties of Inscribable Graphs.'' The other half, which was written by Dillencourt, is mostly on {\it trivalent} inscribable graphs. An ``extended abstract'' of it was submitted to the ACM Computational Geometry Conference, and should also appear as another NEC TM. KEYWORDS: INSCRIBABLE, CIRCUMSCRIBABLE, HAMILTONIAN, PLANAR GRAPHS, POLYHEDRA