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The \(\lambda \) -fold complete 3-uniform hypergraph on v vertices has the edge multiset consisting of \(\lambda \) copies of each 3-element subset of its vertex set. A tight 6-cycle, denoted \(TC_6\) , is a hypergraph with vertex set \(\{a,b,c,d,e,f\}\) and edge set \(\big \{\{a,b,c\}, \{b,c,d\}, \{c,d,e\}, \{d,e,f\}, \{e,f,a\}, \{f,a,b\}\big \}\) . We give necessary and sufficient conditions on v for the existence of a \(TC_{6}\) -decomposition of the \(\lambda \) -fold complete 3-uniform hypergraph on v vertices for any positive integer \(\lambda \) .

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On Tight 6-Cycle Decompositions of Complete 3-Uniform Multi-Hypergraphs

  • 会议论文

  • 发表日期：

    2025年

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  • Jessica A. Bandell,
  • Ryan C. Bunge,
  • Brian D. Darrow,
  • Saad I. El-Zanati,
  • Claire E. Mountain,
  • Levi Neiburger

摘要

The \(\lambda \) -fold complete 3-uniform hypergraph on v vertices has the edge multiset consisting of \(\lambda \) copies of each 3-element subset of its vertex set. A tight 6-cycle, denoted \(TC_6\) , is a hypergraph with vertex set \(\{a,b,c,d,e,f\}\) and edge set \(\big \{\{a,b,c\}, \{b,c,d\}, \{c,d,e\}, \{d,e,f\}, \{e,f,a\}, \{f,a,b\}\big \}\) . We give necessary and sufficient conditions on v for the existence of a \(TC_{6}\) -decomposition of the \(\lambda \) -fold complete 3-uniform hypergraph on v vertices for any positive integer \(\lambda \) .