On degrees of vertices in paradoxical trees Original Research Article

We present some necessary and sufficient conditions (in terms of degrees of vertices) for locally finite tree T=(V,E) to be paradoxical, i.e. to have a partition V=V1∪V2 and one-to-one mappings fi : V→Vi, i=1,2 such that the supremum of the distances between v and fi(v) over v∈V and i=1,2 is finite.