The square of a planar cubic graph is 77-colorable

We prove the conjecture made by G.Wegner in 1977 that the square of every planar, cubic graph is $7$-colorable. Here, $7$ cannot be replaced by $6$

New Bounds for Facial Nonrepetitive Colouring

We prove that the facial nonrepetitive chromatic number of any outerplanar graph is at most 11 and of any planar graph is at most 22.Comment: 16 pages, 5 figure