Coloring count cones of planar graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10448435" target="_blank" >RIV/00216208:11320/22:10448435 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=tH9JiMSkeY" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=tH9JiMSkeY</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/jgt.22767" target="_blank" >10.1002/jgt.22767</a>

Result language
angličtina
Original language name
Coloring count cones of planar graphs
Original language description
For a plane near-triangulation (Formula presented.) with the outer face bounded by a cycle (Formula presented.), let (Formula presented.) denote the function that to each 4-coloring (Formula presented.) of (Formula presented.) assigns the number of ways (Formula presented.) extends to a 4-coloring of (Formula presented.). 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 (Formula presented.) belongs to a certain cone in the space of all functions from 4-colorings of (Formula presented.) to real numbers. We investigate the properties of this cone for (Formula presented.), formulate a conjecture strengthening the Four Color Theorem, and present evidence supporting this conjecture.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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