Halving Steiner 2-designs Original Research Article

A Steiner 2-design image is said to be halvable if the block set can be partitioned into two isomorphic sets. This is equivalent to an edge-disjoint decomposition of a self-complementary graph G on image vertices into image. The obvious necessary condition of those orders image for which there exists a halvable image is that image admits the existence of an image with an even number of blocks. In this paper, we give an asymptotic solution for various block sizes. We prove that for any image or any Mersenne prime k, there is a constant number image such that if image and image satisfies the above necessary condition, then there exists a halvable image. We also show that a halvable image exists for over a half of possible orders. Some recursive constructions generating infinitely many new halvable Steiner 2-designs are also presented.