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Embedding Trees and Cactus Graphs with Integer Edge Lengths on a Compact Integer Grid
Every planar graph can be embedded with crossing-free, straight-line edges on an $O(n) \times O(n)$ integer grid, where $n$ is the number of vertices. It is not known, however, whether integer edge lengths can be guaranteed for all planar graphs (conjectured to be true by Harborth). Kleber conjectur
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