Homogeneous factorisations of Johnson graphs

Abstract

For a graph Γ, subgroups $$M < G\,\leqslant\,{\rm Aut}(\Gamma)$$ , and an edge partition $${\mathcal{E}}$$ of Γ, the pair $$(\Gamma, {\mathcal{E}})$$ is a (G, M)-homogeneous factorisation if M is vertex-transitive on Γ and fixes setwise each part of $${\mathcal{E}}$$ , while G permutes the parts of $${\mathcal{E}}$$ transitively. A classification is given of all homogeneous factorisations of finite Johnson graphs. There are three infinite families and nine sporadic examples.