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DAM
2006
81views more  DAM 2006»
13 years 6 months ago
Equivalence-free exhaustive generation of matroid representations
Abstract. In this paper we present an algorithm for the problem of exhaustive equivalence-free generation of 3-connected matroids which are represented by a matrix over some finite...
Petr Hlinený
EJC
2007
13 years 6 months ago
The structure of 3-connected matroids of path width three
A 3-connected matroid M is sequential or has path width 3 if its ground set E(M) has a sequential ordering, that is, an ordering (e1, e2, . . . , en) such that ({e1, e2, . . . , ek...
Rhiannon Hall, James G. Oxley, Charles Semple
ESA
2006
Springer
112views Algorithms» more  ESA 2006»
13 years 10 months ago
Enumerating Spanning and Connected Subsets in Graphs and Matroids
We show that enumerating all minimal spanning and connected subsets of a given matroid is quasi-polynomially equivalent to the well-known hypergraph transversal problem, and thus ...
Leonid Khachiyan, Endre Boros, Konrad Borys, Khale...
DM
1998
195views more  DM 1998»
13 years 6 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
CRYPTO
2005
Springer
171views Cryptology» more  CRYPTO 2005»
14 years 4 days ago
On Codes, Matroids and Secure Multi-party Computation from Linear Secret Sharing Schemes
Error correcting codes and matroids have been widely used in the study of ordinary secret sharing schemes. In this paper, we study the connections between codes, matroids, and a s...
Ronald Cramer, Vanesa Daza, Ignacio Gracia, Jorge ...