Comparison of MaxSTN and MinSTN orientation path lengths
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Does the proposed longest-path comparison between MaxSTN and MinSTN hold on biconnected graphs with fixed s,t? A counterexample target has nine vertices and ten edges, with output path lengths six and seven respectively for s=1,t=3.
Why it matters and what counts as progress
Why it matters: It tests a concrete ordering claim about two graph algorithms using an exactly specified finite witness.
What counts as progress: An explicit graph where the prescribed MaxSTN and MinSTN outputs violate the proposed comparison, or a comparison theorem for a restricted class.
How the problem developed
- 12 Jun 2026 · Counterexample [1]
K. Papamanthou Gave a nine-vertex, ten-edge biconnected graph with s=1 and t=3 where the longest MaxSTN path has length six and the MinSTN path has length seven, refuting the proposed comparison.
The cited 2026 manuscript presents and refutes the proposed comparison; the sources listed here do not establish an earlier independent formulation.
AI contribution
On a Conjecture for Parameterized st-Orientations
A biconnected graph with nine vertices and ten edges, with s=1 and t=3, gives a longest path of six under MaxSTN and seven under MinSTN, refuting the proposed inequality for these algorithms.
Sources
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Publication dates and editorial changes.
Claude-assisted search finds an st-orientation counterexample