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JCT
2006
62views more  JCT 2006»
14 years 10 months ago
On Rota's conjecture and excluded minors containing large projective geometries
We prove that an excluded minor for the class of GF(q)-representable matroids cannot contain a large projective geometry over GF(q) as a minor.
James F. Geelen, Bert Gerards, Geoff Whittle
LICS
2010
IEEE
14 years 8 months ago
Fixed-Point Definability and Polynomial Time on Graphs with Excluded Minors
We prove that fixed-point logic with counting captures polynomial time on all classes of graphs with excluded minors. That is, for every class C of graphs such that some graph H is...
Martin Grohe
COMBINATORICS
2002
92views more  COMBINATORICS 2002»
14 years 10 months ago
On the Excluded Minors for Matroids of Branch-Width Three
Knowing the excluded minors for a minor-closed matroid property provides a useful alternative characterization of that property. It has been shown in [R. Hall, J. Oxley, C. Semple...
Petr Hlinený
JCT
2010
91views more  JCT 2010»
14 years 8 months ago
Lattice path matroids: The excluded minors
A lattice path matroid is a transversal matroid for which some antichain of intervals in some linear order on the ground set is a presentation. We characterize the minor-closed cla...
Joseph E. Bonin
STOC
1990
ACM
135views Algorithms» more  STOC 1990»
15 years 2 months ago
A Separator Theorem for Graphs with an Excluded Minor and its Applications
ions (Extended Abstract) Noga Alon Paul Seymour Robin Thomas Let G be an n-vertex graph with nonnegative weights whose sum is 1 assigned to its vertices, and with no minor isomorp...
Noga Alon, Paul D. Seymour, Robin Thomas