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G is a 3-regular connected graph of order 1,000. Prove that it is possible to find vertices v1, v2, ... , v100 in G

G is a 3-regular connected graph of order 1,000. Prove that it is possible to find vertices v1, v2, ... , v100 in G such that (a) vi and v; are not connected by an edge for i + j. (b) G {v1, v2, . . . , v100} is connected. ...

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