Berge's Conjecture for Cubic Graphs with Small Colouring Defect

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F25%3A43976278" target="_blank" >RIV/49777513:23520/25:43976278 - isvavai.cz</a>
Result on the web
<a href="https://onlinelibrary.wiley.com/doi/10.1002/jgt.23231" target="_blank" >https://onlinelibrary.wiley.com/doi/10.1002/jgt.23231</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/jgt.23231" target="_blank" >10.1002/jgt.23231</a>

Result language
angličtina
Original language name
Berge's Conjecture for Cubic Graphs with Small Colouring Defect
Original language description
A long standing conjecture of Berge suggests that every bridgeless cubic graph can be expressed as a union of at most five perfect matchings.This conjecture holds for 3-edge-colourable cubic graphs, but remains widely open for graphs that are not 3-edge-coroulable.The aim of this paper is to investigate the validity of Berge conjecture for cubic graphs with small colouring defect. We prove that cubic graphswith colouring defect 3 satisfy the Berge congecture. Moreover, we prove that if the cyclic connectivity is at least four, then four perfect matchings suffice unless the graph is the Petersen graph.
Czech name
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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
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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