Three-coloring triangle-free planar graphs in linear time

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F11%3A10125708" target="_blank" >RIV/00216208:11320/11:10125708 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1145/2000807.2000809" target="_blank" >http://dx.doi.org/10.1145/2000807.2000809</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1145/2000807.2000809" target="_blank" >10.1145/2000807.2000809</a>

Result language
angličtina
Original language name
Three-coloring triangle-free planar graphs in linear time
Original language description
Grotzsch's theorem states that every triangle-free planar graph is 3-colorable, and several relatively simple proofs of this fact were provided by Thomassen and other authors. It is easy to convert these proofs into quadratic-time algorithms to find a 3-coloring, but it is not clear how to find such a coloring in linear time (Kowalik used a nontrivial data structure to construct an O(n log n) algorithm). We design a linear-time algorithm to find a 3-coloring of a given triangle-free planar graph. The algorithm avoids using any complex data structures, which makes it easy to implement. As a by-product, we give a yet simpler proof of Grotzsch's theorem.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
<a href="/en/project/1M0545" target="_blank" >1M0545: Institute for Theoretical Computer Science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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