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Algebraically Closed Fields.- Real Closed Fields.- Semi-Algebraic Sets.- Algebra.- Decomposition of Semi-Algebraic Sets.- Elements of Topology.- Quantitative Semi-algebraic Geometry.- Complexity of… (More)

- Hubert de Fraysseix, János Pach, Richard Pollack
- Combinatorica
- 1990

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 anO(n) space,O(n… (More)

- Saugata Basu, Richard Pollack, Marie-Françoise Roy
- J. ACM
- 1996

In this paper, a new algorithm for performing quantifier elimination from first order formulas over real closed fields in given. This algorithm improves the complexity of the asymptotically fastest… (More)

A system for joining elongate interfitting male and female portions of adjacent tubular members having interengaging locking means on the male and female portions to retain the male portion within… (More)

- Jacob E. Goodman, Richard Pollack
- J. Comb. Theory, Ser. A
- 1980

Abstract 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… (More)

- Jacob E. Goodman, Richard Pollack
- SIAM J. Comput.
- 1983

- Hubert de Fraysseix, János Pach, Richard Pollack
- STOC
- 1988

Answering a question of Rosenstiehl and Tarjan, we show that every plane graph with <italic>n</italic> vertices has a Fáry embedding (i.e., straight-line embedding) on the 2<italic>n</italic> - 4 by… (More)

- Paul Erdös, János Pach, Richard Pollack, Zsolt Tuza
- J. Comb. Theory, Ser. B
- 1989

Abstract We give asymptotically sharp upper bounds for the maximum diameter and radius of (i) a connected graph, (ii) a connected trangle-free graph, (iii) a connected C 4 -free graph with n vertices… (More)

- Pankaj K. Agarwal, Boris Aronov, János Pach, Richard Pollack, Micha Sharir
- Combinatorica
- 1997

A graph is calledquasi-planar if it can be drawn in the plane so that no three of its edges are pairwise crossing. It is shown that the maximum number of edges of a quasi-planar graph withn vertices… (More)

- Jacob E. Goodman, Richard Pollack
- Discrete & Computational Geometry
- 1986

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 on the number of realizable combinatorial types of simple… (More)