volume 33, issue 2, P321-344 2005
DOI: 10.1007/s00454-004-1154-y
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Abstract: We study the properties of Schnyder's realizers and canonical ordering trees of plane graphs. Based on these newly discovered properties, we obtain compact drawings of two styles for any plane graph G with n vertices. First, we show that G has a visibility representation with height at most 15n/16 . This improves the previous best bound of (n − 1). Second, we show that every plane graph G has a straight-line grid embedding on an (n − δ 0 − 1) × (n − δ 0 − 1) grid, where δ 0 is the number of cyclic faces of G …

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