Constructing Regular Self-complementary Uniform Hypergraphs

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Constructing Regular Self-complementary Uniform Hypergraphs

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Title: Constructing Regular Self-complementary Uniform Hypergraphs
Author: Gosselin, Shonda
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 Tayfeh- Rezaie'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 su cient for all k, in the case where t = 1.
Description: AMS Subject Classication Codes: 05C65, 05B05 05E20, 05C85.
URI: http://hdl.handle.net/10680/393
Date: 2011-02-17

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