FINE STRUCTURE OF 4-CRITICAL TRIANGLE-FREE GRAPHS II. PLANAR TRIANGLE-FREE GRAPHS WITH TWO PRECOLORED 4-CYCLES
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10364958" target="_blank" >RIV/00216208:11320/17:10364958 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1137/15M1023397" target="_blank" >http://dx.doi.org/10.1137/15M1023397</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/15M1023397" target="_blank" >10.1137/15M1023397</a>
Alternative languages
Result language
angličtina
Original language name
FINE STRUCTURE OF 4-CRITICAL TRIANGLE-FREE GRAPHS II. PLANAR TRIANGLE-FREE GRAPHS WITH TWO PRECOLORED 4-CYCLES
Original language description
We study 3-coloring properties of triangle-free planar graphs G with two precolored 4-cycles C-1 and C-2 that are far apart. We prove that either every precoloring of C-1 boolean OR C-2 extends to a 3-coloring of G, or G contains one of two special substructures which uniquely determine which 3-colorings of C-1 boolean OR C-2 extend. As a corollary, we prove that there exists a constant D > 0 such that if H is a planar triangle-free graph and if S subset of V(H) consists of vertices at pairwise distances at least D, then every precoloring of S extends to a 3-coloring of H. This gives a positive answer to a conjecture of Dvorak, Kral, and Thomas, and implies an exponential lower bound on the number of 3-colorings of triangle-free planar graphs of bounded maximum degree.
Czech name
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Czech description
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Classification
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
Result continuities
Project
<a href="/en/project/GA14-19503S" target="_blank" >GA14-19503S: Graph coloring and structure</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
SIAM Journal on Discrete Mathematics
ISSN
0895-4801
e-ISSN
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Volume of the periodical
31
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
10
Pages from-to
865-874
UT code for WoS article
000404770300015
EID of the result in the Scopus database
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