Four plane unit vectors generate a $3$-colorable graph

Katherine Eng, Timothy Harris, Mike Krebs +2

We show that given an arbitrary set of four plane unit vectors $v_1,v_2,v_3,v_4$, the Cayley graph generated by $\{\pm v_1,\pm v_2,\pm v_3,\pm v_4\}$ is always $3$-colorable.…