The existence of regular self-complementary 3-uniform hypergraphs

Regular self-complementary uniform hypergraphs

A k-uniform hypergraph with vertex set V and edge set E is called t-subset-regular if every t-element subset of V lies in the same number of elements of E. In this paper we establish a necessary condition on n for there to exist a t-subset-regular selfcomplementary k-uniform hypergraph with n vertices. In addition, we show that this necessary condition is also sufficient in the case k = 3 and t...

Generating self-complementary uniform hypergraphs

A note on 2-subset-regular self-complementary 3-uniform hypergraphs

We show that a 2-subset-regular self-complementary 3-uniform hypergraph with n vertices exists if and only if n ≥ 6 and n is congruent to 2 modulo 4.

Vertex-transitive self-complementary uniform hypergraphs

In this paper we examine the orders of vertex-transitive self-complementary uniform hypergraphs. In particular, we prove that if there exists a vertex-transitive selfcomplementary k-uniform hypergraph of order n, where k = 2 or k = 2 + 1 and n ≡ 1 (mod 2), then the highest power of any prime dividing n must be congruent to 1 modulo 2. We show that this necessary condition is also sufficient in ...

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

we use the recursive method of construction large sets of t-designs given by qiu-rong wu (a note on extending t-designs‎, ‎{em australas‎. ‎j‎. ‎combin.}‎, ‎{bf 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-com...