01497278

j

01497278 Fron\v{c}ek, Dalibor Note on cyclic decompositions of complete bipartite graphs into cubes. Discuss. Math., Graph Theory 19, No.2, 219-227 (1999). 1999 University of Zielona G\'ora Press, Zielona G\'ora EN hypercubes bipartite graph cyclic decomposition cyclic factorization

doi:10.7151/dmgt.1096

http://www.pz.zgora.pl/discuss/gt/19_2/g8.htm

Summary: So far, the smallest complete bipartite graph which was known to have a cyclic decomposition into cubes $Q_d$ of a given dimension $d$ was $K_{d2^{d- 1},d2^{d- 2}}$. We improve this result and show that also $K_{d2^{d- 2},d2^{d- 2}}$ allows a cyclic decomposition into $Q_d$. We also present a cyclic factorization of $K_{8,8}$ into $Q_4$.