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  "problem_id": "vibemathed:eulerian-tour-sampling-barrier",
  "title": "The Arborescence-Sampling Barrier for Eulerian Tours",
  "canonical_statement": "Sampling a nearly uniform Eulerian tour of a directed Eulerian multigraph was stuck at $mn$-type running times coming from arborescence sampling. A randomized algorithm achieves $\\widetilde{O}(m^{3/2})$ worst case, breaking that barrier on sparse graphs.",
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      "title": "arXiv:2605.29566 - Sampling Directed Eulerian Tours in O(m^{3/2}) Time",
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