The Triangle Intersection Problem for Kite Systems

Abstract

The graph …….is called a kite and the decomposition of \(K_n\) into kites is called a kite system. Such systems exist precisely when \(n = 0\) or \(1\) (mod \(8\)). In \(1975\), C. C. Lindner and A. Rosa solved the intersection problem for Steiner triple systems. The object of this paper is to give a complete solution to the triangle intersection problem for kite systems (\(=\) how many triangles can two kite systems of order \(n\) have in common). We show that if \(x \in \{0, 1, 2, \dots, n(n-1)/8\}\), then there exists a pair of kite systems of order \(n\) having exactly \(n\) triangles in common.