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The least possible number of vertices -[UKRMO 2009 Grade 11]

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January 23, 2011
pigeonhole principlegraph theorycombinatorics proposedcombinatorics

Problem Statement

Let GG be a connected graph, with degree of all vertices not less then m≥3m \geq 3, such that there is no path through all vertices of GG being in every vertex exactly once. Find the least possible number of vertices of G.G.
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