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2-dimension ham sandwich theorem for partitioning into three convex pieces. (English) Zbl 0973.52005

Akiyama, Jin (ed.) et al., Discrete and computational geometry. Japanese conference, JCDCG ’98. Tokyo, Japan, December 9-12, 1998. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 1763, 129-157 (2000).
This paper contains a rather complicated proof of the following conjecture which is ascribed to A. Kaneko and M. Kano: “Let \(m\geq 2\), \(n\geq 2\), and \(q\geq 2\) be integers. Let \(S\) be a finite set in the plane which consists of \(nq\) red and \(mq\) blue points, no three on a line. Then \(S\) can be partitioned into \(q\) subsets \(P_{1},\ldots ,P_{q}\) with pairwise disjoint convex hulls such that each subset \(P_{i}\) contains \(n\) red and \(m\) blue points.” The case \(q=2\) is equivalent to the well-known discrete ham sandwich theorem.
For the entire collection see [Zbl 0933.00046].

MSC:

52A37 Other problems of combinatorial convexity
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