“School of Mathematics”

Back to Papers Home
Back to Papers of School of Mathematics

Paper   IPM / M / 17597
School of Mathematics
  Title:   On the total versions of 1-2-3-Conjecture for graphs and hypergraphs
  Author(s):  Leila Maherani (Joint with A. Davoodi)
  Status:   Published
  Journal: Discrete Appl. Math.
  Vol.:  336
  Year:  2023
  Pages:   1-10
  Supported by:  IPM
In 2004, Karo\'nski, \L uczak and Thomason proposed $1$-$2$-$3$-Conjecture: For every nice graph $G$ there is an edge weighting function $ w:E(G)\rightarrow\{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.

Download TeX format
back to top
scroll left or right