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JCT
2011

Hypercube orientations with only two in-degrees

13 years 6 months ago
Hypercube orientations with only two in-degrees
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 = 2n and as + bt = n2n−1 . This is connected to a question arising from constructing a strategy for a “hat puzzle.” AMS 2010 subject classification: 05C20; 00A08; 94B05
Joe Buhler, Steve Butler, Ronald L. Graham, Eric T
Added 14 May 2011
Updated 14 May 2011
Type Journal
Year 2011
Where JCT
Authors Joe Buhler, Steve Butler, Ronald L. Graham, Eric Tressler
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