Do Triangle-Free Planar Graphs have Exponentially Many 3-Colorings?

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10364984" target="_blank" >RIV/00216208:11320/17:10364984 - isvavai.cz</a>

Result on the web

<a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v24i3p47" target="_blank" >http://www.combinatorics.org/ojs/index.php/eljc/article/view/v24i3p47</a>

DOI - Digital Object Identifier

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Result language

angličtina

Original language name

Do Triangle-Free Planar Graphs have Exponentially Many 3-Colorings?

Original language description

Thomassen conjectured that triangle-free planar graphs have an exponential number of 3-colorings. We show this conjecture to be equivalent to the following statement: there exists a positive real α such that whenever G is a planar graph and A is a subset of its edges whose deletion makes G triangle-free, there exists a subset A&apos; of A of size at least α|A| such that G-(A-A&apos;) is 3-colorable. This equivalence allows us to study restricted situations, where we can prove the statement to be true.

Czech name

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Czech description

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Type

J_imp - 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

Result was created during the realization of more than one project. More information in the Projects tab.

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2017

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Electronic Journal of Combinatorics

ISSN

1077-8926

e-ISSN

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Volume of the periodical

24

Issue of the periodical within the volume

3

Country of publishing house

US - UNITED STATES

Number of pages

27

Pages from-to

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UT code for WoS article

000414864700005

EID of the result in the Scopus database

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