  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.
