Advertisement

Improved Bounds for Rota's Basis Conjecture

  • Sally Dong
  • Jim Geelen
Article
  • 16 Downloads

Abstract

We prove that, if B1,...,Bn are disjoint bases of a rank-n matroid, then there are at least \(\frac{n}{{7\log n}}\) disjoint transversals of (B1,...,Bn) that are also bases.

Mathematics Subject Classification (2010)

05B35 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    R. Huang and G.-C. Rota: On the Relations of Various Conjectures on Latin Squares and Straightening Coeffcients, Discrete Math. 128 (1994), 225–236.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    Polymath 12: Rota's Basis Conjecture: Polymath 12. (2017), polymathprojects.org/2017/03/06/rotas-basis-conjecture-polymath-12–2/Google Scholar
  3. [3]
    J. Geelen and K. Webb: On Rota's Basis Conjecture, SIAM Journal of Discrete Math, 21 (2007), 802–804.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    R. Rado: A theorem on Independence Relations. The Quarterly Journal of Mathematics, Col. os-13, no. 1 (1942), 83–89.zbMATHGoogle Scholar
  5. [5]
    P. Erdős and A. Rényi: On Random Matrices, Publications of the Mathematical Institute of the Hungarian Academy of Sciences, Vol. 8, Series A, fasc. 3 (1963), 455–460.Google Scholar

Copyright information

© János Bolyai Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada

Personalised recommendations