Decomposing the cube into paths

作者：Erde Joshua^*

来源：Discrete Mathematics, 2014, 336: 41-45.

DOI：10.1016/j.disc.2014.07.019

• Graph decomposition
• Hypercube

We consider the question of when the n-dimensional hypercube can be decomposed into paths of length k. For odd n it is necessary that k divides n2(n-1) and that k <= n. Anick and Ramras (2013) conjectured that these two conditions are also sufficient for all odd n and prove that this is true for odd n <= 2(32). In this note we prove the conjecture.

• 出版日期2014-12-6