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\centerline{\bf Homework 6, Morally Due Tue April 14, 2020, 3:30PM}
COURSE WEBSITE: \url{http://www.cs.umd.edu/~gasarch/858/S18.html}
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(0 points)
What is your name? Write it clearly.
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(50 points)
In the March 31 recording I gave three proofs of the following theorem:
{\bf Theorem:} For all $k$ there exists $n$ such that, for any $n$ points in the plane no three colinear,
there exists $k$ points that form a convex $k$-gon.
One proof used 5-ary Ramsey.
One proof used 3-ary Ramsey and the coloring
$COL(x,y,z)$ is RED if the number of points inside the x-y-z triangle is RED is even, BLUE if its odd.
One proof used 3-ary Ramsey and the following coloring: let $p_1,\ldots,p_n$ be the points (the ordering
does not correspond to anything geometric, but we need SOME way to order the points).
$COL(p_i,p_j,p_k)$ with $i