Geodesic
More Results on The Smallest One-Realization of A Given Set II
Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 2, pp. 473-487

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Let S be a finite set of positive integers. A mixed hypergraph ℋ is a onerealization of S if its feasible set is S and each entry of its chromatic spectrum is either 0 or 1. The minimum number of vertices, denoted by δ3(S), in a 3-uniform bi-hypergraph which is a one-realization of S was determined in [P. Zhao, K. Diao and F. Lu, More result on the smallest one-realization of a given set, Graphs Combin. 32 (2016) 835–850]. In this paper, we consider the minimum number of edges in a 3-uniform bi-hypergraph which already has the minimum number of vertices with respect of being a minimum bihypergraph that is one-realization of S. A tight lower bound on the number of edges in a 3-uniform bi-hypergraph which is a one-realization of S with δ3(S) vertices is given.
Keywords: mixed hypergraph, feasible set, chromatic spectrum, gap, onerealization 
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     title = {More {Results} on {The} {Smallest} {One-Realization} of {A} {Given} {Set} {II}},
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Diao, Kefeng; Lu, Fuliang; Zhao, Ping. More Results on The Smallest One-Realization of A Given Set II. Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 2, pp. 473-487. http://geodesic.mathdoc.fr/item/DMGT_2019_39_2_a11/