The smallest one-realization of a given set
Abstract
In [The smallest one-realization of a given set, Electronic J. Combin. 19 (2012), 19], we determined the minimum number of vertices of one-realizations of a given finite set S, and constructed the corresponding mixed hypergraphs. In this paper, by finding some of their spanning sub-hypergraphs, we determine the minimum number of D-deges (resp. C-edges) of one-realizations of S. As a result, we partially solve an open problem proposed by Tuza and Voloshin in 2008.
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