In this paper, we show the necessary and sufficient conditions for a complete graph on \(n\) vertices with a hole of size \(v\) (\(K_n \setminus K_v\)) to be decomposed into isomorphic copies of \(K_3\) with a pendant edge.
Citation
D.G. Hoffman, K.S. Kirkpatrick. Another Doyen – Wilson Theorem[J], Ars Combinatoria, Volume 054. 87-96. .