منابع مشابه
The number of generalized balanced lines
Let S be a set of r red points and b = r + 2δ blue points in general position in the plane, with δ ≥ 0. A line l determined by them is balanced if in each open half-plane bounded by l the difference between the number of blue points and red points is δ. We show that every set S as above has at least r balanced lines. The main techniques in the proof are rotations and a generalization, sliding r...
متن کاملOn the Number of Balanced Lines
Given a set of n black and n white points in general position in the plane, a line l determined by them is said to be balanced if each open half-plane bounded by l contains precisely the same number of black points as white points. It is proved that the number of balanced lines is at least n. This settles a conjecture of George Baloglou.
متن کاملA simple proof for the number of balanced lines ∗
Given a set of n blue and n red points in general position in the plane, a line ` determined by them is said to be balanced if each open half-plane bounded by ` contains precisely the same number of blue points as red points. We give a simple proof of the following fact, conjectured by George Baloglou and proved by Pach and Pinchasi [J. Pach and R. Pinchasi. On the number of balanced lines, Dis...
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15 صفحه اولOn the balanced decomposition number
A balanced coloring of a graph G means a triple {P1, P2,X} of mutually disjoint subsets of the vertex-set V (G) such that V (G) = P1⊎P2⊎X and |P1| = |P2|. A balanced decomposition associated with the balanced coloring V (G) = P1⊎P2⊎X of G is defined as a partition of V (G) = V1⊎· · ·⊎Vr (for some r) such that, for every i ∈ {1, · · · , r}, the subgraphG[Vi] of G is connected and |Vi∩P1| = |Vi∩P...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2010
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-010-9253-4