Corpus ID: 126188278

A proof of the Erd\H{o}s-Sands-Sauer-Woodrow conjecture

@article{Bousquet2017APO,
  title={A proof of the Erd\H\{o\}s-Sands-Sauer-Woodrow conjecture},
  author={N. Bousquet and W. Lochet and S. Thomass{\'e}},
  journal={arXiv: Combinatorics},
  year={2017}
}
  • N. Bousquet, W. Lochet, S. Thomassé
  • Published 2017
  • Mathematics
  • arXiv: Combinatorics
  • A very nice result of B\'ar\'any and Lehel asserts that every finite subset $X$ or $\mathbb R^d$ can be covered by $f(d)$ $X$-boxes (i.e. each box has two antipodal points in $X$). As shown by Gy\'arf\'as and P\'alv\H{o}lgyi 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 Erd\H{o}s-Sands-Sauer-Woodrow conjecture : If the… CONTINUE READING
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    References

    SHOWING 1-10 OF 10 REFERENCES
    Domination in transitive colorings of tournaments
    • 16
    • PDF
    On Weighted Kernels of Two Posets
    • 6
    • PDF
    On a lemma of Scarf
    • 13
    Dominating sets in k-majority tournaments
    • 44
    • PDF
    A Fixed-Point Approach to Stable Matchings and Some Applications
    • T. Fleiner
    • Mathematics, Computer Science
    • Math. Oper. Res.
    • 2003
    • 248
    • PDF
    Kernels in Weighted Digraphs
    • 6
    • Highly Influential
    On monochromatic paths in edge-coloured digraphs
    • 127
    On monochromatic paths in m-coloured tournaments
    • Shen Minggang
    • Mathematics, Computer Science
    • J. Comb. Theory, Ser. B
    • 1988
    • 69
    • PDF
    Probabilities Within optimal Strategies for Tournament Games
    • 11
    Covering with Euclidean Boxes
    • 19