This is a problem from Jeff ’s notes - reproduced here for ease. The d-dimensional hypercube...

This is a problem from Jeff ’s notes - reproduced here for ease. The d-dimensional hypercube is the graph defined as follows. There are 2d vertices, each labeled with a different string of d bits. Two vertices are joined by an edge if and only if their labels differ in exactly one bit. See figures in Jeff ’s notes if you need to - but it would be more instructive to draw them yourself and recognize these objects. Recall that a Hamiltonian cycle is a closed walk that visits each vertex in a graph exactly once. Prove that for every integer d ≥ 2, the d-dimensional hypercube has a Hamiltonian cycle.

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Colby Messinger answered 1 year ago

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