FINE STRUCTURE OF 4-CRITICAL TRIANGLE-FREE GRAPHS I. PLANAR GRAPHS WITH TWO TRIANGLES AND 3-COLORABILITY OF CHAINS

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10385413" target="_blank" >RIV/00216208:11320/18:10385413 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1137/15M1023385" target="_blank" >https://doi.org/10.1137/15M1023385</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/15M1023385" target="_blank" >10.1137/15M1023385</a>

Result language
angličtina
Original language name
FINE STRUCTURE OF 4-CRITICAL TRIANGLE-FREE GRAPHS I. PLANAR GRAPHS WITH TWO TRIANGLES AND 3-COLORABILITY OF CHAINS
Original language description
Aksenov proved that in a planar graph G with at most one triangle, every precoloring of a 4-cycle can be extended to a 3-coloring of G. We give an exact characterization of planar graphs with two triangles in which some precoloring of a 4-cycle does not extend. We apply this characterization to solve the precoloring extension problem from two 4-cycles in a triangle-free planar graph in the case that the precolored 4-cycles are separated by many disjoint 4-cycles. The latter result is used in follow-up papers [SIAM J. Discrete Math., 31 (2017), pp. 865-874; SIAM J. Discrete Math., 32 (2018), pp. 94-105] to give detailed information about the structure of 4-critical triangle-free graphs embedded in a fixed surface.
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
—
OECD FORD branch
10101 - Pure mathematics

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)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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