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The VTRC bus company serves cities in the USA. A subset S of the cities is called well-served if it has at least three cities and from every city A in S, one can take a nonstop VTRC bus to at least two different other cities B and C in S (though there is not necessarily a nonstop VTRC bus from B to A or from C to A). Suppose there is a well-served subset S. Prove that there is a well-served subset T such that for any two cities A, B in T, one can travel by VTRC bus from A to B, stopping only at cities in T.
Posted 03 April 2006