Path Bundles on n-Cubes

Abstract

A path bundle is a set of 2^a paths in an n-cube, denoted Q_n, such that every path has the same length, the paths partition the vertices of Q_n, the endpoints of the paths induce two subcubes of Q_n, and the endpoints of each path are complements. This paper shows that a path bundle exists if and only if n > 0 is odd and 0 <= a <= n - ceil[log_2(n + 1)].

Paper

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Changed 17 September 2008