On a coloring problem for the integer grid
Adrian Dumitrescu, Radoš Radoičić · Contemporary mathematics - American Mathematical Society · 2004
János Pach asked whether for any 2-coloring of the points of the integer grid in the plane, there exist arbitrary long sequences of consecutive collinear points of the same color. We answer this question in the negative for the plane, and more generally for any number of dimensions. More precisely, we show that...