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The Smallest One-Realization of a Given Set III

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Abstract

In Zhao et al. (Electron J Combin 19:\({\sharp}\) P19, 2012), 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 \({\mathcal{D}}\) -deges (resp. \({\mathcal{C}}\) -edges) of one-realizations of S. As a result, we partially solve an open problem proposed by Tuza and Voloshin (Bolyai Society Mathematical Studies, vol. 17, pp. 235–255. Springer, Berlin, 2008).

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Authors and Affiliations

  1. School of Science, Linyi University, Linyi, Shandong, 276005, China

    Kefeng Diao & Ping Zhao

  2. Sch. Math. Sci.& Lab. Math. Com. Sys., Beijing Normal University, Beijing, 100875, China

    Kaishun Wang

Authors
  1. Kefeng Diao
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  2. Ping Zhao
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  3. Kaishun Wang
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Correspondence to Kaishun Wang.

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Diao, K., Zhao, P. & Wang, K. The Smallest One-Realization of a Given Set III. Graphs and Combinatorics 30, 875–885 (2014). https://doi.org/10.1007/s00373-013-1322-z

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  • DOI: https://doi.org/10.1007/s00373-013-1322-z

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