Optimal st-orientations for plane triangulations

Huaming Zhang () and Xin He ()
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Huaming Zhang: University of Alabama in Huntsville
Xin He: SUNY at Buffalo

Journal of Combinatorial Optimization, 2009, vol. 17, issue 4, No 2, 367-377

Abstract: Abstract For plane triangulations, it has been proved that there exists a plane triangulation G with n vertices such that for any st-orientation of G, the length of the longest directed paths of G in the st-orientation is $\geq\lfloor\frac{2n}{3}\rfloor$ (Zhang and He in Lecture Notes in Computer Science, vol. 3383, pp. 425–430, 2005). In this paper, we prove the bound $\frac{2n}{3}$ is optimal by showing that every plane triangulation G with n-vertices admits an st-orientation with the length of its longest directed paths bounded by $\frac{2n}{3}+O(1)$ . In addition, this st-orientation is constructible in linear time. A by-product of this result is that every plane graph G with n vertices admits a visibility representation with height $\le\frac{2n}{3}+O(1)$ , constructible in linear time, which is also optimal.

Keywords: st-orientation; Plane triangulation (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1007/s10878-007-9119-8

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