Abstract
Let m ≥ 2, n ≥ 2 and q ≥ 2 be positive integers. Let S r and S b be two disjoint sets of points in the plane such that no three points of S r ∪ S b are collinear, |S r | = nq, and |S b | = mq. This paper shows that Kaneko and Kano’s conjecture is true, i.e., S r ∪ S b can be partitioned into q subsets P 1,P 2,...,P q satisfying that: (i) conv(P i ) ∩ conv(P j ) = ∅ for all 1 ≤ i < j ≤ q; (ii) |P i ∩ S r |= n and |P i ∩ S b | = m for all 1 ≤ i ≤ q. This is a generalization of 2-dimension Ham Sandwich Theorem.
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References
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© 2000 Springer-Verlag Berlin Heidelberg
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Ito, H., Uehara, H., Yokoyama, M. (2000). 2-Dimension Ham Sandwich Theorem for Partitioning into Three Convex Pieces. In: Akiyama, J., Kano, M., Urabe, M. (eds) Discrete and Computational Geometry. JCDCG 1998. Lecture Notes in Computer Science, vol 1763. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-46515-7_11
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DOI: https://doi.org/10.1007/978-3-540-46515-7_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67181-7
Online ISBN: 978-3-540-46515-7
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