A family of $t$-regular ‎self-complementary $k$-hypergraphs

Document Type : Research Paper

Authors

1 University of zanjan

2 Department of Mathematics, University of Zanjan

Abstract

We use the recursive method of construction large sets of t-designs given by Qiu-rong Wu [A note on extending t-designs‎, Australas‎. ‎J‎. ‎Combin.‎, 4 (1991) 229--235.], and present a similar method for constructing $t$-subset-regular‎ ‎self-complementary $k$-uniform hypergraphs of order $v$‎. ‎As an‎ ‎application we show the existence of a new family of $2$-subset-regular‎ ‎self-complementary $4$-uniform hypergraphs with $v=16m+3$‎.

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References

[1] G. B. Khosrovshahi and R. Laue, t-Designs, t≤3, in: Handbook of combinatorial designs, 2nd ed. (C. J. Colb ourn and J. H. Dinitz, eds.), CRC press, Bo ca Raton, (2007) 98-110.
[2] G. B. Khosrovshahi, R. Laue and B. Tayfeh-Rezaie, On large sets of t-designs of size four, Bayreuth. Math. Schr., 74 (2005) 136-144.
[3] G. B. Khosrovshahi and B. Tayfeh-Rezaie, Ro ot cases of large sets of t-designs, Discrete Math., 263 (2003) 143-155.
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[6] E. S. Kramer and D. M. Mesner, t-designs on hyp ergraphs, Discrete Math., 15 (1976) 263-296.
[7] Qiu-rong Wu, A note on extending t-designs, Australas. J. Combin., 4 (1991) 229-235.
[8] A. Szymanski, A note on self-complementary 4-uniform hyp ergraphs, Opuscula Math., 25 (2005) 319-323.

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History

  • Receive Date: 25 November 2015
  • Revise Date: 09 August 2016
  • Accept Date: 10 August 2016
  • Published Online: 01 March 2017

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