Self-Complementary Non-Uniform Hypergraphs

Gosselin, Shonda

doi:10.1007/s00373-011-1070-x

Cited by 3 publications

(2 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Then the factors of

scriptF

are t ‐subset regular k ‐hypergraphs with t and λ listed in Table . The reader is referred to for more examples and results on t ‐subset regular hypergraphs. (2)Recall that a large set of t ‐

(n, k, λ)

designs of size N , denoted by

LS [N] (t, k, n)

, is a partition of the set of all k ‐subsets of an n ‐set into block sets of N disjoint t ‐

(n, k, λ)

designs, where

N λ = {false(}_{k - t}^{n - t})

. Let

scriptF

be one of the factorizations in Theorem .…”

Section: The Main Resultsmentioning

confidence: 99%

Edge‐transitive homogeneous factorizations of complete uniform hypergraphs

Chen

2017

Journal of Graph Theory

View full text Add to dashboard Cite

For a finite set V and a positive integer k with k≤n:=|V|, letting Vfalse{kfalse} be the set of all k‐subsets of V, the pair scriptKnk:=false(V,Vfalse{kfalse}false) is called the complete k‐hypergraph on V, while each k‐subset of V is called an edge. A factorization of the complete k‐hypergraph Knk of index s≥2, simply a (k,s)‐factorization of order n, is a partition {E1,E2,…,Es} of the edges into s disjoint subsets such that each k‐hypergraph (V,Ei), called a factor, is a spanning subhypergraph of Knk. Such a factorization is homogeneous if there exist two transitive subgroups G and M of the symmetric group of degree n such that G induces a transitive action on the set {E1,E2,…,Es} and M lies in the kernel of this action. In this article, we give a classification of homogeneous factorizations of Knk that admit a group acting transitively on the edges of Knk. It is shown that, for 6≤2k≤n and s≥2, there exists an edge‐transitive homogeneous (k,s)‐factorization of order n if and only if (n,k,s) is one of (32, 3, 5), (32, 3, 31), (33, 4, 5), ()2d,3,false(2d−1false)false(2d−1−1false)3, and (q+1,3,2), where d≥3 and q is a prime power with q≡1(mod4).

show abstract

“…Then the factors of

scriptF

(n, k, λ)

designs of size N , denoted by

LS [N] (t, k, n)

, is a partition of the set of all k ‐subsets of an n ‐set into block sets of N disjoint t ‐

(n, k, λ)

designs, where

N λ = {false(}_{k - t}^{n - t})

. Let

scriptF

be one of the factorizations in Theorem .…”

Section: The Main Resultsmentioning

confidence: 99%

Edge‐transitive homogeneous factorizations of complete uniform hypergraphs

Chen

2017

Journal of Graph Theory

View full text Add to dashboard Cite

show abstract

“…For a nonempty subset S of positive integers, a S-hypergraph on V is a hypergraph with vertex set V and edge set E = s∈S E s , where E s is a non-empty set of s-subsets of V . The complement of a S-hypergraph H(V, E), denoted by H c (V, E c ) is the S-hypergraph on V whose edge set consists of the subsets of V with cardinality in S which do not lie in E [9]. The degree of a vertex v in a hypergraph H, denoted by d(v), is the number of edges containing v in H. Definition 2.1.…”

Section: Preliminaries and Notationsmentioning

confidence: 99%

Tensor join of hypergraphs and its spectra

Vishnupriya¹,

Rajkumar²

2022

Preprint

View full text Add to dashboard Cite

In this paper, we introduce three operations on hypergraphs by using tensors. We show that these three formulations are equivalent and we commonly call them as the tensor join. We show that any hypergraph can be viewed as a tensor join of hypergraphs. Tensor join enable us to obtain several existing and new classes of operations on hypergraphs. We compute the adjacency, the Laplacian, the normalized Laplacian spectrum of weighted hypergraphs constructed by this tensor join. Also we deduce some results on the spectra of hypergraphs in the literature. As an application, we construct several pairs of the adjacency, the Laplacian, the normalized Laplacian cospectral hypergraphs by using the tensor join.

show abstract

A Note on Non-reconstructible 3-Hypergraphs

Kocay

2016

Graphs and Combinatorics

View full text Add to dashboard Cite

Self-Complementary Non-Uniform Hypergraphs

Cited by 3 publications

References 14 publications

Edge‐transitive homogeneous factorizations of complete uniform hypergraphs

Edge‐transitive homogeneous factorizations of complete uniform hypergraphs

Tensor join of hypergraphs and its spectra

A Note on Non-reconstructible 3-Hypergraphs

Contact Info

Product

Resources

About