Results 31 to 40 of about 4,009 (153)
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
Covering-Based Rough Sets on Eulerian Matroids [PDF]
Journal of Applied Mathematics, 2013 Rough set theory is an efficient and essential tool for dealing with vagueness and granularity in information systems. Covering-based rough set theory is proposed as a significant generalization of classical rough sets. Matroid theory is a vital structure with high applicability and borrows extensively from linear algebra and graph theory.
Bin Yang, Ziqiong Lin, William Zhu
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Analyzing single-valued neutrosophic fuzzy graphs through matroid perspectives
Ain Shams Engineering JournalWe hope to present this paper on the emergence of a novel category of matroids derived from single-valued neutrosophic (SVN) fuzzy-graphs. The findings of this study make a substantial contribution to both matroid theory and the field of neutrosophic ...
S.M. Balaji, D. Meiyappan, R. Sujatha
doaj +1 more source
Osculating geometry and higher‐order distance Loci
Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract We discuss the problem of optimizing the distance function from a given point, subject to polynomial constraints. A key algebraic invariant that governs its complexity is the Euclidean distance degree, which pertains to first‐order tangency. We focus on the data locus of points possessing at least one critical point of the distance function ...
Sandra Di Rocco +2 more
wiley +1 more source
Rough sets and matroidal contraction [PDF]
, 2012 Rough sets are efficient for data pre-processing in data mining. As a generalization of the linear independence in vector spaces, matroids provide well-established platforms for greedy algorithms.
Wang, Jingqian, Zhu, William
core
On Disjoint Common Bases in Two Matroids [PDF]
SIAM Journal on Discrete Mathematics, 2011 Summary: We prove two results on packing common bases of two matroids. First, we show that the computational problem of common base packing reduces to the special case where one of the matroids is a direct sum of uniform matroids. Second, we give a counterexample to a conjecture of Chow, which proposed a sufficient condition for the existence of a ...
Harvey, Nicholas J. A. +2 more
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A tropical approach to rigidity: Counting realisations of frameworks
Journal of the London Mathematical Society, Volume 113, Issue 2, February 2026.Abstract A realisation of a graph in the plane as a bar‐joint framework is rigid if there are finitely many other realisations, up to isometries, with the same edge lengths. Each of these finitely many realisations can be seen as a solution to a system of quadratic equations prescribing the distances between pairs of points.
Oliver Clarke +6 more
wiley +1 more source
Some characteristics of matroids through rough sets [PDF]
, 2012 At present, practical application and theoretical discussion of rough sets are two hot problems in computer science. The core concepts of rough set theory are upper and lower approximation operators based on equivalence relations. Matroid, as a branch of
Su, Lirun, Zhu, William
core
, 2002 We consider a problem of optimizing convex functionals over matroid bases. It is richly expressive and captures certain quadratic assignment and clustering problems.
Onn, Shmuel
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A characterization of the base-matroids of a graphic matroid
Contributions to Discrete Mathematics, 2010 Let M=(E,F) be a matroid on a set E and B one of its bases. A closed set θ⊆E is saturated with respect to B when |θ∩B|≤r(θ), where r(θ) is the rank of θ. The collection of subsets I of E such that |I∩θ|≤r(θ) for every closed saturated set θ turns out to be the family of independent sets of a new matroid on E, called base-matroid and denoted by MB.
MAFFIOLI, FRANCESCO, ZAGAGLIA, NORMA
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