Decomposition of \(\lambda K_v\) into Kites and \(4\)-Cycles

Abstract

Given a collection of graphs \(\mathcal{H}\), an \(\mathcal{H}\)-decomposition of \(\lambda K_v\) is a decomposition of the edges of \(\lambda K_v\) into isomorphic copies of graphs in \(\mathcal{H}\). A kite is a triangle with a tail consisting of a single edge. In this paper, we investigate the decomposition problem when \(\mathcal{H}\) is the set containing a kite and a \(4\)-cycle, that is, this paper gives a complete solution to the problem of decomposing \(\lambda K_v\) into \(r\) kites and \(s\) \(4\)-cycles for every admissible values of \(v\), \(r,\lambda\), and \(s\).