Journal of Guangxi Normal University(Natural Science Edition) ›› 2021, Vol. 39 ›› Issue (4): 93-98.doi: 10.16088/j.issn.1001-6600.2020092702

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Decompositions of λ-fold Complete Bipartite 3-uniform Hypergraphs λK(3)n,n into Hypergraph Triangular Bipyramid

ZHAO Hongtao*, LIU Zhiwei   

  1. School of Mathematics and Physics, North China Electric Power University, Beijing 102206 , China
  • Revised:2020-11-14 Online:2021-07-25 Published:2021-07-23

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Abstract: This paper studies the question of decompositions of λ-fold complete bipartite 3-uniform hypergraphs λK(3)n,n into hypergraph triangular bipyramid. This kind of decomposition is denoted by Sλ(3,TB,n,n). Firstly, it is proved that the necessary condition of its existence is 6|λn2(n-1),2|λn and n≥3. Then, it is proved that the necessary conditions are also sufficient except for two possible exceptions of n=10,14.

Key words: hypergraph decomposition, complete bipartite 3-uniform hypergraphs, triangular bipyramid, super edge, base block

CLC Number: 

  • O157.5
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