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mn line segments that connect n given points

Source: Czech and Slovak Olympiad 1989, National Round, Problem 2

September 13, 2024
combinatoricscombinatorial geometrygraph theory

Problem Statement

There are mnmn line segments in a plane that connect nn given points. Prove that a sequence V0V_0, V1V_1, ......, VmV_m of different points can be selected from them such that Vi−1V_{i-1} and ViV_i are connected by a line (1≤i≤m1 \le i \le m).
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