Disjoint cycles and spanning graphs of hypercubes

AbstractThe aim of this paper is to prove that double starlike trees are embedable into hypercubes, which answers an open question posed by Ivan Havel (Časopis Pěst. Mat. 109 (1984) 135). For this, a theorem about partitioning the hypercubes into vertex-disjoint cycles of even length is first proved. This theorem is then used to prove that a new family of graphs, the MD-graphs, are embedable into hypercubes. Finally, we prove that the double starlike trees are themselves embedable into the MD-graphs, so are in the hypercubes