, Volume 19, Issue 4, pp 595-604

Embedding into Rectilinear Spaces

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Abstract.

We show that the problem whether a given finite metric space (X,d) can be embedded into the rectilinear space R m can be formulated in terms of m -colorability of a certain hypergraph associated with (X,d) . This 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 problem. 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 ≤ 3 .

Received March 19, 1996, and in revised form March 14, 1997.