5 papers
A sequel to the adventure of RGB-tilings to explore the Four Color Theorem
Shu-Chung Liu
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 methodolog…
A renewal approach to prove the Four Color Theorem unplugged, Part I: RGB-tilings on maximal planar graphs
Shu-Chung Liu
This is the first part of three episodes to demonstrate a renewal approach for proving the Four Color Theorem without checking by a computer. The second and the third episodes have…
A renewal approach to prove the Four Color Theorem unplugged, Part II: R/G/B Kempe chains in an extremum non-4-colorable MPG
Shu-Chung Liu
This is the second part of three episodes to demonstrate a renewal approach for proving the Four Color Theorem without checking by a computer. The first and the third episodes have…
A renewal approach to prove the Four Color Theorem unplugged, Part III: Diamond routes, canal lines and -adjustments
Shu-Chung Liu
This is the last part of three episodes to demonstrate a renewal approach for proving the Four Color Theorem without checking by a computer. The first and the second episodes have…
Left-modular elements
Shu-Chung Liu, Bruce Sagan
Left-modularity is a concept that generalizes modularity in lattice theory. In this paper, we give a characterization of left-modular elements and derive two formulae for the chara…