On embeddings of CAT(0) cube complexes into products of trees

Victor Chepoi, Mark F. Hagen

We prove that the contact graph of a 2-dimensional CAT(0) cube complex $\mathbf{X}$ of maximum degree $\Delta$ can be coloured with at most $\epsilon (\Delta )=M{\Delta }^{26}$ colours, for a fixed constant $M$…