Graphs and Combinatorics

, Volume 32, Issue 2, pp 835–850 | Cite as

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

  • Ping Zhao
  • Kefeng Diao
  • Fuliang Lu
Original Paper


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.


Mixed hypergraph Feasible set Chromatic spectrum One-realization 



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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Copyright information

© Springer Japan 2015

Authors and Affiliations

  1. 1.School of ScienceLinyi UniversityLinyiChina

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