Homogeneous factorisations of Johnson graphs

Authors:
Maria Cristeta Cuaresma;Michael Giudici;Cheryl E. Praeger
Affiliations:
Institute of Mathematical Sciences and Physics, University of the Philippines - Los Banos, Los Banos, The Philippines;School of Mathematics and Statistics, The University of Western Australia, Crawley, Australia 6009;School of Mathematics and Statistics, The University of Western Australia, Crawley, Australia 6009
Venue:
Designs, Codes and Cryptography
Year:
2008

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Homogeneous factorisations of complete graphs with edge-transitive factors

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Abstract

For a graph Γ, subgroups $$M , and an edge partition $${\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.