Show that the graph $G$ is $2$ colorable

Question

Show that the graph $G$ is $2$ colorable which is define with vertex set $\mathbb Z^2$ where $(m,n)$ is adjacent to $(j,k)$ if $(m,n)\pm(1,0)=(j,k)$ or $(m,n)\pm(0,1)=(j,k)$.

I just draw a portion of the graph and it seems easily two colorable, like if I color a vertex with red and a different color (like blue) with all of it's adjacent vertices. But couldn't write it in a formal way.

I was doubt to write it in plain english because there are infintely many vertices to color, it would be nice if anyone show me the right way.

Answer 1

HINT: Consider whether $m+n$ is even or odd.