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arXiv · 2606.14539

On a Conjecture for Parameterized st-Orientations

Charalampos Papamanthou
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Abstract

MaxSTN and MinSTN -- proposed by Papamanthou and Tollis (TCS 2008, JGAA 2010) -- are two algorithms for producing $st$-orientations of biconnected graphs with long and short longest paths respectively. Based on extensive experiments on planar and non-planar graphs of up to 5,000 nodes, it was conjectured that $\ell_{\max} \geq \ell_{\min}$ for every biconnected graph $G$, where $\ell_{\max}$ and $\ell_{\min}$ denote the longest-path lengths of the two orientations. This paper disproves this conjecture by exhibiting a biconnected graph on 9 vertices for which MaxSTN yields $\ell_{\max}=6$ while MinSTN yields $\ell_{\min}=7$, regardless of how ties are broken in either algorithm.

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Charalampos Papamanthou. 2026-06-12. On a Conjecture for Parameterized st-Orientations. https://arxiv.org/abs/2606.14539

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