Primitive C4 ${C}_{4}$‐decompositions of Kn−I ${K}_{n}-I$.

A decomposition C ${\mathscr{C}}$ of a graph G $G$ is primitive if no proper, nontrivial subset of C ${\mathscr{C}}$ is a decomposition of an induced subgraph of G $G$. An unresolved question posed by Asplund et al. in a recent publication involves the existence of primitive decompositions of cocktail party graphs into cycles of length 4, which is resolved by this paper. [ABSTRACT FROM AUTHOR]