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» Matroids with nine elements
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FOCS
2006
IEEE
15 years 10 months ago
Algebraic Structures and Algorithms for Matching and Matroid Problems
We present new algebraic approaches for several wellknown combinatorial problems, including non-bipartite matching, matroid intersection, and some of their generalizations. Our wo...
Nicholas J. A. Harvey
DM
1998
195views more  DM 1998»
15 years 3 months ago
On basis-exchange properties for matroids
We give a counterexample to a conjecture by Wild about binary matroids. We connect two equivalent lines of research in matroid theory: a simple type of basis-exchange property and ...
Joseph E. Bonin
COMBINATORICA
2008
62views more  COMBINATORICA 2008»
15 years 4 months ago
The toric ideal of a graphic matroid is generated by quadrics
Describing minimal generating sets of toric ideals is a well-studied and difficult problem. Neil White conjectured in 1980 that the toric ideal associated to a matroid is generated...
Jonah Blasiak
ESA
2011
Springer
260views Algorithms» more  ESA 2011»
14 years 4 months ago
On Variants of the Matroid Secretary Problem
We present a number of positive and negative results for variants of the matroid secretary problem. Most notably, we design a constant-factor competitive algorithm for the “rando...
Shayan Oveis Gharan, Jan Vondrák
ESA
2007
Springer
105views Algorithms» more  ESA 2007»
15 years 10 months ago
Finding Branch-Decompositions and Rank-Decompositions
Abstract. We present a new algorithm that can output the rankdecomposition of width at most k of a graph if such exists. For that we use an algorithm that, for an input matroid rep...
Petr Hlinený, Sang-il Oum