Covering the hypercube with a bounded number of disjoint snakes

Abstract

We present a construction of an induced cycle in then-dimensional hypercubeI[n] (n≥2), and a subgroup ℌ n ofI[n] considered as the group ℤ n2 , such that |ℌ n |≤16 and the induced cycle uses exactly one element of every coset of ℌ n . This proves that for anyn≥2 the vertices ofI[n] can be covered using at most 16 vertex-disjoint induced cycles.

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Wojciechowski, J. Covering the hypercube with a bounded number of disjoint snakes. Combinatorica 14, 491–496 (1994). https://doi.org/10.1007/BF01302970

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AMS subject classification code (1980)

  • 05 C 35
  • 94 B 25