Decompositions of n-Cube into 2^mn-Cycles

2018/04/04 by Tapadia, S. A., Waphare, B. N., Borse, Y. M.
#05C70 #68R10 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1804.01243

Abstract

It is known that the n-dimensional hypercube Q_n, for n even, has a decomposition into k-cycles for k=n, 2n, 2^l with 2 ≤ l ≤ n. In this paper, we prove that Q_n has a decomposition into 2^mn-cycles for n ≥ 2^m. As an immediate consequence of this result, we get path decompositions of Q_n as well. This gives a partial solution to a conjecture posed by Ramras and also, it solves some special cases of a conjecture due to Erde.

Related

• Long path and cycle decompositions of even hypercubes
• Decomposition of hypercubes into sunlet graphs
• Decomposing the cube into paths
• Generalization of Cycle Decompositions of Even Dimensional Hypercubes on d-Dimensional Toruses
• Edge Decompositions of Hypercubes by Paths