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Article
Coloring count cones of planar graphs
arxiv
Document Type
Article
Disciplines
Publication Version
Submitted Manuscript
Publication Date
7-10-2019
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.
Copyright Owner
The Authors
Copyright Date
2019
Language
en
File Format
application/pdf
Citation Information
Zdenek Dvorak and Bernard Lidicky. "Coloring count cones of planar graphs" arxiv (2019) Available at: http://works.bepress.com/bernard-lidicky/61/
This is a pre-print made available through arxiv: https://arxiv.org/abs/1907.04066.