Decomposing hypercubes into regular connected subgraphs
A. V. Sonawane, Y. M. Borse · Discrete Mathematics Algorithms and Applications · 2016
It is known that the [Formula: see text]-dimensional hypercube [Formula: see text] for [Formula: see text] with [Formula: see text] can be decomposed into two spanning bipancyclic subgraphs [Formula: see text] and [Formula: see text] such that [Formula: see text] is [Formula: see text]-regular and [Formula: see text]-connected for [Formula: see text] In this paper, we prove that if [Formula: see text] with [Formula: see text] and at most one [Formula: see text] odd, then [Formula: see text] can be decomposed into [Formula: see text] spanning subgraphs [Formula: see text], [Formula: see text] such that [Formula: see text] is [Formula: see text]-regular and [Formula: see text]-connected for [Formula: see text]