On inequivalent representations of matroids over finite fields
Journal of Combinatorial Theory Series B
The excluded minors for GF(4)-representable matroids
Journal of Combinatorial Theory Series B
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Branch-width and well-quasi-ordering in matroids and graphs
Journal of Combinatorial Theory Series B
Graph Minors. XX. Wagner's conjecture
Journal of Combinatorial Theory Series B - Special issue dedicated to professor W. T. Tutte
Trees, grids, and MSO decidability: from graphs to matroids
Theoretical Computer Science - Parameterized and exact computation
Branch-width, parse trees, and monadic second-order logic for matroids
Journal of Combinatorial Theory Series B
Vertex-minors, monadic second-order logic, and a conjecture by Seese
Journal of Combinatorial Theory Series B
Some Hard Problems on Matroid Spikes
Theory of Computing Systems
Computing representations of matroids of bounded branch-width
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Decomposition width of matroids
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Decomposition width of matroids
Discrete Applied Mathematics
Deciding first order properties of matroids
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
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In this paper we look at complexity aspects of the following problem (matroid representability) which seems to play an important role in structural matroid theory: Given a rational matrix representing the matroid M, the question is whether M can be represented also over another specific finite field. We prove this problem is hard, and so is the related problem of minor testing in rational matroids. The results hold even if we restrict to matroids of branch-width three.