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

0571157 - ÚI 2024 RIV NL eng J - Journal Article
Davoodi, Akbar - Maherani, L.
On the total versions of 1-2-3-Conjecture for graphs and hypergraphs.
Discrete Applied Mathematics. Roč. 336, 15 September 2023 (2023), s. 1-10. ISSN 0166-218X. E-ISSN 1872-6771
R&D Projects: GA ČR(CZ) GA19-08740S
Institutional support: RVO:67985807
Keywords : Vertex coloring * Edge weighting * Hypergraphs
OECD category: Applied mathematics
Impact factor: 1.1, year: 2022
Method of publishing: Limited access
https://doi.org/10.1016/j.dam.2023.03.021

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.
Permanent Link: https://hdl.handle.net/11104/0342442