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

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Advance Math

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

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