A generalization of 2-dimension Ham Sandwich Theorem
Let m greater than or equal to 2, n greater than or equal to 2, and q greater than or equal to 2 be positive integers. Let S, and Sb be two disjoint sets of points in the plane such that no three points of S-r boolean OR S-b are collinear, /S-r/ = nq, and /S-b/ = mq. This paper shows that Kaneko and Kano's conjecture is true. i.e., there are q disjoint convex regions of the plain such that each region includes n points of S-r and m points of S-b. This is a generalization of 2-dimension Ham Sandwich Theorem.
ham sandwich theorem plane convex partition