Abstract
Let $f$ be a face of a plane graph $G$. The Three and Five Color Theorem proved here states that the vertices of $G$ can be colored with five colors, and using at most three colors on the boundary of $f$. With this result the well-known Five Color Theorem for planar graphs can be strengthened, and a relative coloring conjecture of Kainen can be settled except for a single case which happens to be a paraphrase of the Four Color Conjecture. Some conjectures are presented which are intermediate in strength to the Four Color Conjecture and the Three and Five Color Theorem.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
