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More Result on the Smallest One-Realization of a Given Set

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Abstract

For any set S of positive integers, a mixed hypergraph \({\mathcal {H}}\) is a one-realization of S if its feasible set is S and each entry of its chromatic spectrum is either 0 or 1. In this paper, a tight lower bound on the minimum number of edges of 3-uniform bi-hypergraphs which are one-realizations of a given set S is presented. As a result, we partially solve an open problem proposed by Bujtás and Tuza in 2008.

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Acknowledgments

We thanks the referees for helpful suggestions. This research is supported by NSF of Shandong Province (ZR2013AL009, 2014ZRB019GU), promotive research fund for excellent young and middle-aged scientists of Shandong province(Grant no. BS2013DX026), AMEP of Linyi University, NSF of China (11301251).

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Authors and Affiliations

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

    Ping Zhao, Kefeng Diao & Fuliang Lu

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  1. Ping Zhao
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  2. Kefeng Diao
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  3. Fuliang Lu
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Correspondence to Kefeng Diao.

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Zhao, P., Diao, K. & Lu, F. More Result on the Smallest One-Realization of a Given Set. Graphs and Combinatorics 32, 835–850 (2016). https://doi.org/10.1007/s00373-015-1603-9

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  • DOI: https://doi.org/10.1007/s00373-015-1603-9

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