Abstract
A visibility representation of a graph G is to represent the nodes of G with non-overlapping horizontal line segments such that the line segments representing any two distinct adjacent nodes are vertically visible to each other. If G is a plane graph, i.e., a planar graph equipped with a planar embedding, a visibility representation of G has the additional requirement of reflecting the given planar embedding of G. For the case that G is an n-node four-connected plane graph, we give an O(n)-time algorithm to produce a visibility representation of G with height at most \(\left\lceil\frac{n}{2}\right\rceil+2\left\lceil\sqrt{\frac{n-2}{2}}\right\rceil\). To ensure that the first-order term of the upper bound is optimal, we also show an n-node four-connected plane graph G, for infinite number of n, whose visibility representations require heights at least \(\frac{n}{2}\).
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Chen, CY., Hung, YF., Lu, HI. (2009). Visibility Representations of Four-Connected Plane Graphs with Near Optimal Heights. In: Tollis, I.G., Patrignani, M. (eds) Graph Drawing. GD 2008. Lecture Notes in Computer Science, vol 5417. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00219-9_8
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DOI: https://doi.org/10.1007/978-3-642-00219-9_8
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