Decomposition of hypercubes into regular connected bipancyclic subgraphs
Y. M. Borse, S. A. Kandekar · Discrete Mathematics Algorithms and Applications · 2015
In this paper, we consider the problem of decomposing the edge set of the hypercube Qn into two spanning, regular, connected, bipancyclic subgraphs. We prove that if n = n1 + n2 with n1 ≥ 2 and n2 ≥ 2, then the edge set of Qn can be decomposed into two spanning, bipancyclic subgraphs H1 and H2 such that Hi is ni-regular and ni-connected for i = 1, 2.