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splitting of planar polygons, largest integer of triangles

Source: JBMO 2016 Shortlist C4

October 14, 2017
JBMOcombinatoricsgraph theoryplanar graphtriangulation

Problem Statement

A splitting of a planar polygon is a fi nite set of triangles whose interiors are pairwise disjoint, and whose union is the polygon in question. Given an integer n≥3n \ge 3, determine the largest integer mm such that no planar nn-gon splits into less than mm triangles.
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