MathDB

Let

\{x_n\}

be a Van Der Corput series,that is,if the binary representation of

n

\sum a_{i}2^{i}

then

x_n=\sum a_i2^{-i-1}

.Let

V

be the set of points on the plane that have the form

(n,x_n)

.Let

G

be the graph with vertex set

V

that is connecting any two points

(p,q)

if there is a rectangle

R

which lies in parallel position with the axes and

R\cap V= \{p,q\}

.Prove that the chromatic number of

G

is finite.

Problem Statement