Corpus ID: 43288744

A proof of the Erdős Sands Sauer

@inproceedings{Bousquet2017APO,
  title={A proof of the Erdős Sands Sauer},
  author={N. Bousquet and W. Lochet and S. Thomass{\'e}},
  year={2017}
}
A very nice result of Bárány and Lehel asserts that every finite subset X or R can be covered by f(d) X-boxes (i.e. each box has two antipodal points in X). As shown by Gyárfás and Pálvőlgyi 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 colored with k… CONTINUE READING

References

SHOWING 1-10 OF 15 REFERENCES
Domination in transitive colorings of tournaments
  • 16
  • PDF
On a Lemma of Scarf
  • 33
On Weighted Kernels of Two Posets
  • 6
  • PDF
Monochromatic sinks in nearly transitive arc-colored tournaments
  • 10
A Fixed-Point Approach to Stable Matchings and Some Applications
  • T. Fleiner
  • Mathematics, Computer Science
  • Math. Oper. Res.
  • 2003
  • 248
  • PDF
Dominating sets in k-majority tournaments
  • 44
  • PDF
Kernels in Weighted Digraphs
  • 6
On monochromatic paths in edge-coloured digraphs
  • 127
Monochromatic Paths and at Most 2-Coloured Arc Sets in Edge-Coloured Tournaments
  • 17