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

Self-Complementary Hypergraphs

In this thesis, we survey the current research into self-complementary hypergraphs, and present several new results. We characterize the cycle type of the permutations on n elements with order equal to a power of 2 which are k-complementing. The k-complementing permutations map the edges of a k-uniform hypergraph to the edges of its complement. This yields a test to determine whether a finite p...

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.

A note on k-uniform self-complementary hypergraphs of given order

We prove that a k-uniform self-complementary hypergraph of order n exists, if and only if ( n k ) is even.

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 ...