Premium
The 1‐2‐3‐Conjecture for Hypergraphs
Author(s) -
Kalkowski Maciej,
Karoński Michał,
Pfender Florian
Publication year - 2017
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.22100
Subject(s) - mathematics , conjecture , combinatorics , discrete mathematics
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 article, we show that such a weighting is possible from the weight set { 1 , 2 , … , max { 5 , 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.