Well-covered triangulations: Part IV

Abstract

A graph G is said to be well-covered if every maximal independent set of vertices has the same cardinality. A plane (simple) graph in which each face is a triangle is called a (plane) triangulation. In the first of a sequence of three papers the authors proved that there are no 5-connected plane well-covered triangulations. Clearly, the only plane triangulation which is exactly 2-connected is the triangle K3. Two subsequent papers culminated in the proof that there are exactly four well-covered plane triangulations which are exactly 4-connected.It is the aim of the present paper to complete the characterization of well-covered plane triangulations by characterizing the infinite family of those well-covered triangulations of the plane which are exactly 3-connected.