Results 21 to 30 of about 4,000 (161)
Matroids with a modular 4-point line [PDF]
, 2014 A result of Seymour implies that any 3-connected matroid with a modular 3-point line is binary. We prove a similar characterization for 3-connected matroids with modular 4-point lines.
Kapadia, Rohan
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European Journal of Combinatorics, 1988 Let \(M=(E,{\mathcal F})\) be a matroid on the underlying set E (\({\mathcal F}\) is the collection of flats of M). A simple matroid \(A=(S,{\mathcal T})\) is the adjoint of M if \(r_ M(E)=r_ A(S)\) and there exists an injection \(\phi\) : \({\mathcal F}\to {\mathcal T}\) such that for \(F_ 1,F_ 2\in {\mathcal F}\), if \(F_ 1\subseteq F_ 2\) then ...
Bixby, Robert E., Coullard, Collette R.
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Minor-closed classes of binary functions [PDF]
Discrete Mathematics & Theoretical Computer ScienceBinary functions are a generalisation of the cocircuit spaces of binary matroids to arbitrary functions. Every rank function is assigned a binary function, and the deletion and contraction operations of binary functions generalise matroid deletion and ...
Benjamin R. Jones
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
Graphic Splitting of Cographic Matroids
Discussiones Mathematicae Graph Theory, 2015 In this paper, we obtain a forbidden minor characterization of a cographic matroid M for which the splitting matroid Mx,y is graphic for every pair x, y of elements of M.
Pirouz Naiyer
doaj +1 more source
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
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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.
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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
Matroid union — Graphic? Binary? Neither?
Discrete Applied Mathematics, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Csehi, Csongor György, Recski, András
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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.
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