A sequel to the adventure of RGB-tilings to explore the Four Color Theorem

Abstract

An approach of using RGB-tilings for proving the Four Color Theorem discussed in three previous work is expanded in this paper. A novel methodology and revisions for the methodology in the three aforementioned papers are discussed, and a previously derived result involving three degree-five vertices in a triangular graph is improved. Moreover, a treatment of a novel topic for a graph with six vertices of degree 5 in a dumbbell shape is presented.