The fiber dimension of a graph

Graphs on integer points of polytopes whose edges come from a set of allowed differences are studied. It is shown that any simple graph can be embedded in that way. The minimal dimension of such a representation is the fiber dimension of the given graph. The fiber dimension is determined for various classes of graphs and an upper bound in terms of the chromatic number is stated.Comment: 10 pages, 4 figure

References 1. H.-J. Bandelt, V. Chepoi, M. Laurent, Embedding into rectilinear spaces, Discrete Comput.

Lattice embeddings of trees. (English summary