Hypercube orientations with only two in-degrees

Authors:
Joe Buhler;Steve Butler;Ron Graham;Eric Tressler
Affiliations:
Center for Communications Research, La Jolla, CA 92121, United States;Department of Mathematics, UCLA, Los Angeles, CA 90095, United States;Department of Computer Science and Engineering, University of California, San Diego, La Jolla, CA 92093, United States;HRL Laboratories, LLC, Malibu, CA 90265, United States
Venue:
Journal of Combinatorial Theory Series A
Year:
2011

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Abstract

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 obvious necessary conditions hold. Namely, we need 0=