A proof of the Erdős-Sands-Sauer-Woodrow conjecture

  title={A proof of the Erdős-Sands-Sauer-Woodrow conjecture},
  author={N. Bousquet and W. Lochet and S. Thomass{\'e}},
  journal={J. Comb. Theory, Ser. B},
  • N. Bousquet, W. Lochet, S. Thomassé
  • Published 2019
  • Philosophy, Computer Science, Mathematics
  • J. Comb. Theory, Ser. B
  • Abstract A very nice result of Barany and Lehel asserts that every finite subset X or R d can be covered by h ( d ) X-boxes (i.e. each box has two antipodal points in X). As shown by Gyarfas and Palvőlgyi this result would follow from the following conjecture: If a tournament admits a partition of its arc set into k quasi-orders, then its domination number is bounded in terms of k. This question is in turn implied by the Erdős–Sands–Sauer–Woodrow conjecture: If the arcs of a tournament T are… CONTINUE READING
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