Almost Self-Complementary Uniform Hypergraphs

Abstract

A k-uniform hypergraph (k-hypergraph) is almost self-complementary if it is isomorphic with its complement in the complete k-uniform hypergraph minus one edge. We prove that an almost self-complementary k-hypergraph of order n exists if and only if (nk)$\left({\matrix{ n \cr k \cr } } \right)$ is odd.

Keywords

• uniform hypergraph
• 035c