Hypercube orientations with only two in-degrees

Details Hypercube orientations with only two in-degrees Hypercube orientations with only two in-degrees

2010-07-14

arxiv.org/abs/1007.2311v1

Mathematics

Combinatorics

9 pages, 4 figures

Scientific paper

We consider the problem of orienting the edges of the $n$-dimensional hypercube so only two different in-degrees $a$ and $b$ occur. We show that this can be done, for two specified in-degrees, if and only if an obvious necessary condition holds. Namely, there exist non-negative integers $s$ and $t$ so that $s+t=2^n$ and $as+bt=n2^{n-1}$. This is connected to a question arising from constructing a strategy for a "hat puzzle."

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