No abstract

We prove that every tree T = (V, E) on n vertices with edges of unit length can be embedded in the plane with distortion O( √ n); that is, we construct a mapping f : where ρ(u, v) denotes the length of the path from u to v in T . The embedding is described by a simple and easily computable formula. This is asymptotically optimal in the worst case. We also construct interesting optimal embeddings for a special class of trees (fans consisting of paths of the same length glued together at a common vertex).Communicated by: P. Mutzel and M. Jünger;

No abstract

No abstract

In this paper we show that the recognition problem for C-I graphs of posets is NP-complete. On the other hand, we prove that induced subgraphs of C-I graphs are exactly complements of comparability graphs, and hence the recognition problem for induced subgraphs of C-I graphs of posets is polynomial.