Weak and Strong Versions of the 1-2-3 Conjecture for Uniform Hypergraphs

[摘要] Given an $r$-uniform hypergraph $H=(V,E)$ and a weight function $\omega:E\to\{1,\dots,w\}$, a coloring of vertices of~$H$, induced by~$\omega$, is defined by $c(v) = \sum_{e\ni v} w(e)$ for all $v\in V$. If there exists such a coloring that is strong (tha

[学科分类] 离散数学和组合数学