On the total versions of 1-2-3-Conjecture for graphs and hypergraphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F23%3A00571157" target="_blank" >RIV/67985807:_____/23:00571157 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.dam.2023.03.021" target="_blank" >https://doi.org/10.1016/j.dam.2023.03.021</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.dam.2023.03.021" target="_blank" >10.1016/j.dam.2023.03.021</a>

Result language
angličtina
Original language name
On the total versions of 1-2-3-Conjecture for graphs and hypergraphs
Original language description
In 2004, Karoński, Łuczak and Thomason proposed 1-2-3-Conjecture: For every nice graph G there is an edge weighting function w:E(G)→{1,2,3} such that the induced vertex coloring is proper. After that, the total versions of this conjecture were suggested in the literature and recently, Kalkowski et al. have generalized this conjecture to hypergraphs. In this paper, some previously known results on the total versions are improved. Moreover, an affirmative answer is given to the conjecture for some well-known families of hypergraphs like complete n-partite hypergraphs, paths, cycles, theta hypergraphs and some geometric planes. Also, these hypergraphs are characterized based on the corresponding parameter.
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
10102 - Applied mathematics

Project
<a href="/en/project/GA19-08740S" target="_blank" >GA19-08740S: Embedding, Packing and Limits in Graphs</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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