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 \(t \geq 2n\). 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.