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

A hypergraph is said to be -partite -uniform if its vertex set can be partitioned into non-empty sets so that every edge in the edge set, consists of precisely one vertex from each set,. It is denoted as or if for. In this paper we define -partite self-complementary and almost self-complementary -uniform hypergraph. We prove that, there exists an -partite self-complementary -uniform hypergraph where for if and only if at least one of is even. And we prove that, there exists an -pasc where for if and only if are odd. Further, we analyze the cycle structure of complementing permutations of -partite self-complementary -uniform hypergraphs and -partite almost self-complementary -uniform hypergraphs.

Abstract licence: CC BY-NC

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