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least cardinal a cover of class of n-gons by triangles

Source: IMAR 2017 p4

September 27, 2018
combinatorial geometrycombinatoricsgeometrypolygon

Problem Statement

Let nn be an integer greater than or equal to 33, and let PnP_n be the collection of all planar (simple) nn-gons no two distinct sides of which are parallel or lie along some line. For each member PP of PnP_n, let fn(P)f_n(P) be the least cardinal a cover of PP by triangles formed by lines of support of sides of PP may have. Determine the largest value fn(P)f_n(P) may achieve, as PP runs through PnP_n.
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