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Game on a perfect bipartite graph

Source: 2017 Korean Winter Program Practice Test 1 Day 1 #2

January 18, 2017
combinatoricsCombinatorial gamesgraph theory

Problem Statement

There are m≥2m \ge 2 blue points and n≥2n \ge 2 red points in three-dimensional space, and no four points are coplanar. Geoff and Nazar take turns, picking one blue point and one red point and connecting the two with a straight-line segment. Assume that Geoff starts first and the one who first makes a cycle wins. Who has the winning strategy?
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