01423752

j

01423752 Sonntag, Martin Teichert, Hanns-Martin Sum numbers of hypertrees. Discrete Math. 214, No.1-3, 285-290 (2000). 2000 Elsevier Science B.V. (North-Holland), Amsterdam EN labeling sum hypergraph sum number hypertree

doi:10.1016/S0012-365X(99)00307-6

Summary: A hypergraph ${\cal H}$ is a sum hypergraph iff there are a finite $S\subset \bbfN^+$ and $d_{\min},d_{\max}\in \bbfN^+$ with $1< d_{\min}\le d_{\max}$ such that ${\cal H}$ is isomorphic to the hypergraph ${\cal H}_{d_{\min}d_{\max}}(S)= (V,{\cal E})$ where $V:= S$ and $${\cal E}:= \Biggl\{e\subseteq S: d_{\min}\le |e|\le d_{\max}\text{ and }\sum_{x\in e}x\in S\Biggr\}.$$ We prove that the sum number of a hypertree (:= connected, non-trivial and cycle-free hypergraph) is equal to $1$, if a certain condition for the cardinalities of the edges is fulfilled.