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- W1985263293 abstract "The following problem was posed in the 27th International Mathematics Olympiad (1986): One is given a finite set of points P n in the plane, each point having integer coordinates. Is it always possible to colour some of the points red and the remaining points white in such a way that, for any straight line L parallel to either one of the coordinate axes, the difference (in absolute value) between the number of white points and red points on L is not greater than 1? It is not hard to see that the answer to the above question is “yes”. In this note we generalize this result, and show that P n can be coloured with m ( m ⩾2) colours in such a way that for any straight line parallel to either one of the coordinate axes, the difference (in absolute value) between the number of points coloured i and the number of points coloured j is at most 1, 1⩽ i < j ⩽ m . A conjecture for the higher dimensional case is presented." @default.
- W1985263293 created "2016-06-24" @default.
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- W1985263293 date "1990-07-01" @default.
- W1985263293 modified "2023-09-28" @default.
- W1985263293 title "A note on balanced colourings for lattice points" @default.
- W1985263293 doi "https://doi.org/10.1016/0012-365x(90)90227-9" @default.
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