4-CRITICAL GRAPHS ON SURFACES WITHOUT CONTRACTIBLE ({= 4)-CYCLES

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F14%3A10283293" target="_blank" >RIV/00216208:11320/14:10283293 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1137/130920952" target="_blank" >http://dx.doi.org/10.1137/130920952</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/130920952" target="_blank" >10.1137/130920952</a>

Result language
angličtina
Original language name
4-CRITICAL GRAPHS ON SURFACES WITHOUT CONTRACTIBLE ({= 4)-CYCLES
Original language description
We show that if G is a 4-critical graph embedded in a fixed surface S so that every contractible cycle has length at least 5, then G can be expressed as G = G'boolean OR G(1)boolean OR G(2)boolean OR ... boolean OR G(k), where vertical bar V (C')verticalbar| and k are bounded by a constant (depending linearly on the genus of Sigma) and C-1, ... , C-k are graphs (of unbounded size) whose structure we describe exactly. The proof is computer assisted-we use a computer to enumerate all plane 4-critical graphs of girth 5 with a precolored cycle of length at most 16 that are used in the basic case of the inductive proof of the statement.
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
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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
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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