Constructing regular self-complementary uniform hypergraphs

Abstract

In this paper, we examine the possible orders of t-subset-regular selfcomplementary k-uniform hypergraphs, which form examples of large sets of two isomorphic t-designs. We reformulate Khosrovshahi and TayfehRezaie's necessary conditions on the order of these structures in terms of the binary representation of the rank k, and these conditions simplify to a more transparent relation between the order n and rank k in the case where k is a sum of consecutive powers of 2. Moreover, we present new constructions for 1-subset-regular self-complementary uniform hypergraphs, and prove that these necessary conditions are sucient for all k, in the case where t = 1.

-partite self-complementary and almost self-complementary -uniform hypergraphs

“…A. Symański, A. P. Wojda [1][2][3] and S. Gosselin [4], independently characterized n and k for which there exist k-uniform self-complementary hypergraphs of order n and gave the structure of corresponding complementing permutations.…”

Edge‐transitive homogeneous factorizations of complete uniform hypergraphs

“…Self-complementary uniform hypergraphs have been extensively studied, see [14,16,[18][19][20]25] and the references therein for self-complementary graphs, and see [7][8][9]23,24] for self-complementary uniform hypergraphs. In particular, Peisert [21] gave a complete classification for symmetric (i.e.…”