Campus Units

Mathematics

Document Type

Article

Publication Version

Submitted Manuscript

Publication Date

7-10-2019

Journal or Book Title

arxiv

Abstract

For a plane near-triangulation G with the outer face bounded by a cycle C, let n⋆G denote the function that to each 4-coloring ψ of C assigns the number of ways ψ extends to a 4-coloring of G. The block-count reducibility argument (which has been developed in connection with attempted proofs of the Four Color Theorem) is equivalent to the statement that the function n⋆G belongs to a certain cone in the space of all functions from 4-colorings of C to real numbers. We investigate the properties of this cone for |C|=5, formulate a conjecture strengthening the Four Color Theorem, and present evidence supporting this conjecture.

Comments

This is a pre-print made available through arxiv: https://arxiv.org/abs/1907.04066.

Copyright Owner

The Authors

Language

en

File Format

application/pdf

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