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JCT
2006
62views more  JCT 2006»
13 years 4 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
13 years 2 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»
13 years 4 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»
13 years 3 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»
13 years 8 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