MathDB

For any 2 convex polygons

S

and

T

, if all the vertices of

S

are vertices of

T

, call

S

a sub-polygon of

T

. I. Prove that for an odd number

n \geq 5

, there exists

m

sub-polygons of a convex

n

-gon such that they do not share any edges, and every edge and diagonal of the

n

-gon are edges of the

m

sub-polygons. II. Find the smallest possible value of

m

Problem Statement