Local version of Vizing's theorem for multigraphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F24%3A00138609" target="_blank" >RIV/00216224:14330/24:00138609 - isvavai.cz</a>
Result on the web
<a href="https://onlinelibrary.wiley.com/doi/full/10.1002/jgt.23155" target="_blank" >https://onlinelibrary.wiley.com/doi/full/10.1002/jgt.23155</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/jgt.23155" target="_blank" >10.1002/jgt.23155</a>

Result language
angličtina
Original language name
Local version of Vizing's theorem for multigraphs
Original language description
Extending a result of Christiansen, we prove that every multigraph G = ( V , E ) $G=(V,E)$ admits a proper edge colouring ? : E ? { 1 , 2 , ? } $phi :Eto {1,2,ldots ,}$ which is local, that is, ? ( e ) ? max { d ( x ) + π ( x ) , d ( y ) + π ( y ) } $phi (e)leqslant max {d(x)+pi (x),d(y)+pi (y)}$ for every edge e $e$ with end-points x , y ? V $x,yin V$, where d ( z ) $d(z)$ (resp. π ( z ) $pi (z)$) denotes the degree of a vertex z $z$ (resp. the maximum edge multiplicity at z $z$). This is derived from a local version of the Fan Equation.
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

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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