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Peter A. Linnell---Previous VTRMC Problem

A Problem from a Previous VTRMC
Peter A. Linnell
Virginia Polytechnic Institute & State University

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.

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Posted 03 April 2006

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