A Partial Kite System of Order $n$ Can be Embedded in a Kite System OF Order $8n+9$

Abstract

In this paper, it is shown that a partial edge-disjoint decomposition of $K_n$ into kites (that is, into copies of $K_3$ with a pendant edge attached) can be embedded in a complete edge-disjoint decomposition of $K_{4t+9}$ into kites for all even $t\ge 2n$. The proof requires first proving another interesting result, a generalization of an embedding result on symmetric latin squares by L. D. Andersen, following a result by A. Cruse.