Decompositions of Complete Uniform Multipartite Hypergraphs

Finally, we introduce a property of hypergraphs which relates coloring of the hypergraphs to decomposition of complete multipartite graphs and give some ...

In recent years, researchers have studied the existence of complete uniform hypergraphs into small-order hypergraphs. In particular, results on small ...

3-Uniform 4-Path Decompositions of ... - ScholarWorks@UARK

of hypergraphs for decomposing K. (3) v . The complete multipartite 3-uniform hypergraph is defined with vertex set V = U1 ∪U2 ∪U3, where U1,U2,U3 are ...

6-Cycle decompositions of complete 3-uniform hypergraphs

In this paper we give necessary and sufficient conditions for a decomposition of the complete 3-uniform hypergraph of order n into 6-cycles. 1 Introduction. A ...

Factorizations of complete multipartite hypergraphs - ScienceDirect

This conjecture was finally settled by Baranyai [8]. Let K n × m 3 denote the 3-uniform hypergraph with vertex partition { V i : i ∈ [ n ] } , ...

The -Acyclic Hypergraph Decompositions of Complete Uniform ...

Introduction. Decomposition I. Decomposition II. Concluding Remarks. X Zhang. Monash University. The α-Acyclic Hypergraph Decompositions of Complete Uniform ...

On loose 3-cycle decompositions of complete 4-uniform hypergraphs

We next define some notation for certain types of multipartite-like 4-uniform hypergraphs. Let A, B, C, D be pairwise disjoint sets. The hypergraph with vertex.

arXiv:2102.02869v1 [math.CO] 4 Feb 2021

of factorization of complete uniform multipartite hypergraphs, but here we aim to solve this ... Hilton, Hamilton decompositions of complete ...

Decompositions of complete uniform hypergraphs into Hamilton ...

So a Hamilton Berge cycle has n edges. Let K. (k) n denote the complete k-uniform hypergraph on n vertices. Clearly ...

On Hamilton cycle decompositions of complete multipartite graphs ...

Akinola, affirm that the thesis, On Hamilton cycle decompositions of complete multipartite graphs which are both cyclic and symmetric, meets the high academic ...

decompositions of complete multipartite graphs into gregarious 6 ...

Abstract. The complete multipartite graph Kn(2t) having n partite sets of size 2t, with n ≥ 6 and t ≥ 1, is shown to have a decomposition into.

Packing, covering and decomposing of a complete uniform ...

References · Baranyai, Z.: On the Factorization of the Complete Uniform Hypergraph. · Folkman, J. · Lonc, Z.: Decompositions of Hypergraphs into Hyperstars. · Lonc, ...

Hamiltonian decompositions of hypergraphs

a WJ-Hamiltonian decomposition of the complete 4-uniform bipartite hypergraph, ... hypergraphs and some complete multipartite 3-uniform hypergraphs. The ...

(PDF) Factorizations of Complete Multipartite Hypergraphs

... complete h-uniform hypergraph. In connection with Kirkman's. schoolgirl problem [14], Sylvester conjectured that Kh. nis 1-factorable if and only if h n.

Cyclic partitions of complete nonuniform hypergraphs and complete ...

Such results have applications to cyclic decompositions of complete multipartite k-uniform hypergraphs, which will be discussed in Section 3. The main ...

On decompositions of complete hypergraphs - CiteSeerX

Given an r-uniform hypergraph H, let fr(H) denote the minimum number of complete r- partite r-uniform hypergraphs needed to partition the ...

"On Hamilton cycle decompositions of complete multipartite graphs ...

Such decompositions are known to exist for complete graphs and families of other graphs. In this work, we show the existence of cyclic n-symmetric Hamilton ...

4-Hyperclique Decompositions of 3-Hyperdistance ...

The technique yields a decomposition not only of a distance multihypergraph but also one of a complete 3-uniform multipartite hypergraph. Corollary 2.16 ...

3-UNIFORM HYPERGRAPHS: DECOMPOSITION AND REALIZATION

Proof. Clearly, if H is an empty hypergraph, a prime hypergraph, or a complete graph, then all the strong modules of H are trivial.

Decomposing complete 3-uniform hypergraph K_{n}^{(3)} into 7-cycles

Wang, Hamiltonian decompositions of complete bipartite hypergraphs,. Acta Math. Appl. Sin. 4 (2001), 563–566. [5] H. Jordon, G. Newkirk, 4-cycle ...