Results 21 to 30 of about 4,003 (147)
Matroidal Structure of Rough Sets Based on Serial and Transitive Relations
Journal of Applied Mathematics, 2012 The theory of rough sets is concerned with the lower and upper approximations of objects through a binary relation on a universe. It has been applied to machine learning, knowledge discovery, and data mining. The theory of matroids is a generalization of
Yanfang Liu, William Zhu
doaj +1 more source
Matroid toric ideals: complete intersection, minors and minimal systems of generators [PDF]
, 2015 In this paper, we investigate three problems concerning the toric ideal associated to a matroid. Firstly, we list all matroids $\mathcal M$ such that its corresponding toric ideal $I_{\mathcal M}$ is a complete intersection.
Alfonsín, Jorge Luis Ramírez +1 more
core +2 more sources
Nullity and Loop Complementation for Delta-Matroids [PDF]
, 2012 We show that the symmetric difference distance measure for set systems, and more specifically for delta-matroids, corresponds to the notion of nullity for symmetric and skew-symmetric matrices. In particular, as graphs (i.e., symmetric matrices over GF(2)
Bouchet A. +6 more
core +1 more source
The highly connected even-cycle and even-cut matroids [PDF]
, 2018 The classes of even-cycle matroids, even-cycle matroids with a blocking pair, and even-cut matroids each have hundreds of excluded minors. We show that the number of excluded minors for these classes can be drastically reduced if we consider in each ...
Grace, Kevin, van Zwam, Stefan H. M.
core +3 more sources
Short Cocircuits in Binary Matroids
European Journal of Combinatorics, 1987 The authors' summary: ``Given a simple graph G having vertex set V, it is obvious that for any spanning tree T, there is an edge of T whose fundamental cutset has size at most \(| V| -1\). We extend this result to matroids. Call a cocircuit of a matroid M short if its size is at most the rank of M.
Bixby, Robert E., Cunningham, William H.
openaire +1 more source
An extended formulation for the 1‐wheel inequalities of the stable set polytope
Networks, Volume 75, Issue 1, Page 86-94, January 2020., 2020 Abstract The 1‐wheel inequalities for the stable set polytope were introduced by Cheng and Cunningham. In general, there is an exponential number of these inequalities. We present a new polynomial size extended formulation of the stable set relaxation that includes the odd cycle and 1‐wheel inequalities.
Sven de Vries +2 more
wiley +1 more source
Complementation, Local Complementation, and Switching in Binary Matroids [PDF]
, 2020 In 2004, Ehrenfeucht, Harju, and Rozenberg showed that any graph on a vertex set $V$ can be obtained from a complete graph on $V$ via a sequence of the operations of complementation, switching edges and non-edges at a vertex, and local complementation ...
Oxley, James, Singh, Jagdeep
core +3 more sources
Matroid union — Graphic? Binary? Neither?
Discrete Applied Mathematics, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Csehi, Csongor György, Recski, András
openaire +3 more sources
The moduli space of matroids [PDF]
, 2018 In the first part of the paper, we clarify the connections between several algebraic objects appearing in matroid theory: both partial fields and hyperfields are fuzzy rings, fuzzy rings are tracts, and these relations are compatible with the respective ...
Baker, Matthew, Lorscheid, Oliver
core +2 more sources
Connected Hyperplanes in Binary Matroids
Journal of Combinatorial Theory, Series B, 2000 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
McNulty, Jennifer, Wu, Haidong
openaire +2 more sources