MathDB

6

Part of 2015 Chile National Olympiad

Problems(1)

2 color painting of closed curve (Chile 2015 L2 P6)

Source:

10/5/2021
On the plane, a closed curve with simple auto intersections is drawn continuously. In the plane a finite number is determined in this way from disjoint regions. Show that each of these regions can be completely painted either white or blue, so that every two regions that share a curve segment at its edges, they always have different colors.
Clarification: a car intersection is simple if looking at a very small disk around from her, the curve looks like a junction ×\times.
combinatoricsColoring