Answering a question of Rosenstiehl and Tarjan, we show that every plane graph withn vertices has a Fáry embedding (i.e., straight-line embedding) on the 2n−4 byn−2 grid and provide an O(n) space,O(n logn) time algorithm to effect this embedding.Expand

We give asymptotically sharp upper bounds for the maximum diameter and radius of a connected graph, a connected trangle-free graph, and a connected C 4 -free graph with n vertices.Expand

We give a new upper bound onnd(d+1)n on the number of realizable order types of simple configurations ofn points inRd, and ofn2d2n onthe number of combinatorial types ofsimple configurations.Expand

On montre que l'equivalence de semi-espace est la notion appropriee pour distinguer les proprietes des configurations qui se relient a l'orientation, la separation et la convexite

We classify nondegenerate plane configurations by attaching, to each such configuration of n points, a periodic sequence of permutations of {1, 2, …, n } which satisfies some simple conditions; this classification turns out to be appropriate for questions involving convexity.Expand