Question: Define a cube graph as follows. Let the following be the set of vertices (you can think that each vertex is labeled by a string

Define a cube graph as follows. Let the following be the set of vertices (you can think that each vertex is labeled by a string of bits of length 3):

V = {000, 001, 010, 011, 100, 101, 110, 111}. We have an edge between vertices u and v iff u and v differ by one bit and are the same in the other two positions.

Prove that the cube graph is bipartite

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