Let G be either a complete graph of odd order or a complete bipartite graph in which each vertex partition has an even number of vertices. In this paper, we determine the set of triples (p, q, r), with p, q, r > 0, for which there exists a decomposition of G into p paths, q stars, and r cycles, each of which has 4 edges.
Shyu, T. W. (2021). Decompositions of Complete Bipartite Graphs and Complete Graphs into Paths, Stars, and Cycles with Four Edges Each. Discussiones Mathematicae - Graph Theory, 41(2), 451–468. https://doi.org/10.7151/dmgt.2197