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Number of pairwise disjoint monochromatic segments

Source: Donova Mathmatical Olympiad 2010

February 11, 2012
inductiongeometryperimetercombinatorics proposedcombinatorics

Problem Statement

All sides and diagonals of a convex nn-gon, n≥3n\ge 3, are coloured one of two colours. Show that there exist [n+13]\left[\frac{n+1}{3}\right] pairwise disjoint monochromatic segments.
(Two segments are disjoint if they do not share an endpoint or an interior point).
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