A Generalization of 2-Dimension Ham Sandwich Theorem

Hiro ITO  Hideyuki UEHARA  Mitsuo YOKOYAMA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E84-A   No.5   pp.1144-1151
Publication Date: 2001/05/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
Ham Sandwich Theorem,  plane,  partition,  convex,  

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Let m 2, n 2, and q 2 be positive integers. Let Sr and Sb be two disjoint sets of points in the plane such that no three points of Sr Sb are collinear, |Sr| = nq, and |Sb| = 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 Sr and m points of Sb. This is a generalization of 2-dimension Ham Sandwich Theorem.