The 1-2-3 Conjecture for Hypergraphs
Combinatorics
2016-05-20 v2
Abstract
A weighting of the edges of a hypergraph is called vertex-coloring if the weighted degrees of the vertices yield a proper coloring of the graph, i.e., every edge contains at least two vertices with different weighted degrees. In this paper we show that such a weighting is possible from the weight set {1,2,...,r+1} for all hypergraphs with maximum edge size r>3 and not containing edges solely consisting of identical vertices. The number r+1 is best possible for this statement. Further, the weight set {1,2,3,4,5} is sufficient for all hypergraphs with maximum edge size 3, up to some trivial exceptions.
Cite
@article{arxiv.1308.0611,
title = {The 1-2-3 Conjecture for Hypergraphs},
author = {Maciej Kalkowski and Michał Karoński and Florian Pfender},
journal= {arXiv preprint arXiv:1308.0611},
year = {2016}
}
Comments
12 pages