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How to draw a planar graph on a grid. (English) Zbl 0728.05016
The authors show that every plane graph with n vertices has a straight- line embedding on the 2n-4 by n-2 grid, and provide an O(n) space, O(n.log n) time algorithm for finding the embedding. On the other hand, they prove that any set F, which can support a straight-line embedding of every planar graph of size n, has cardinality at least \(n+(1- o(1))\sqrt{n}\). This settles a problem of B. Mohar.

MSC:
05C10 Planar graphs; geometric and topological aspects of graph theory
05C35 Extremal problems in graph theory
68R10 Graph theory (including graph drawing) in computer science
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