Well-covered triangulations: Part IV

作者：Finbow Arthur S^*; Hartnell Bert L; Nowakowski Richard J; Plummer Michael D

来源：Discrete Applied Mathematics, 2016, 215: 71-94.

DOI：10.1016/j.dam.2016.06.030

• Well-covered graph
• Maximal independent set
• 3-connected well-covered triangulation

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 K-3. 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.

• 出版日期2016-12-31