EMBEDDING INTO RECTILINEAR SPACES

We show that the problem whether a given finite metric space (X, d) ca n be embedded into the rectilinear space R-m can be formulated in term s of m-colorability of a certain hypergraph associated with (X, d). Th is is used to close a gap in the proof of an assertion of Bandelt and Chepoi [2] on certain critical metric spaces for this embedding proble m. We also consider the question of determining the maximum number of equidistant points that can be placed in the m-dimensional rectilinear space and show that this number is equal to 2m for m less than or equ al to 3.