Results 191 to 200 of about 4,266 (227)
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SIAM Journal on Discrete Mathematics, 1991
Summary: This paper begins with a short discussion of the general principles of Rigidity Theory. The main interest is the combinatorial part of this subject: generic rigidity. While generic rigidity has several combinatorial characterizations in dimensions one and two, these characterizations have not been able to be extended to characterizations of ...
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Summary: This paper begins with a short discussion of the general principles of Rigidity Theory. The main interest is the combinatorial part of this subject: generic rigidity. While generic rigidity has several combinatorial characterizations in dimensions one and two, these characterizations have not been able to be extended to characterizations of ...
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On fuzzifying matroids: Dual matroids and spanning
Journal of Intelligent & Fuzzy Systems, 2015In this paper, we prove that not all of fuzzifying matroids have dual matroids. Then we give a sufficient and necessary condition such that a fuzzifying matroid has dual matroid. We also present the notion of spanning of fuzzifying matroids and prove that a fuzzifying matroid with dual matroid can be reproduced by its dual matroid and its spanning ...
Shoubin Sun, Zhenyu Xiu, Lingqiang Li
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Combinatorics, Probability and Computing, 2008
Semple and Welsh [5] introduced the concept of correlated matroids, which relate to conjectures by Grimmett and Winkler [2], and Pemantle [4], respectively, that the uniformly random forest and the uniformly random connected subgraph of a finite graph have the edge-negative-association property. In this paper, we extend results of Semple and Welsh, and
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Semple and Welsh [5] introduced the concept of correlated matroids, which relate to conjectures by Grimmett and Winkler [2], and Pemantle [4], respectively, that the uniformly random forest and the uniformly random connected subgraph of a finite graph have the edge-negative-association property. In this paper, we extend results of Semple and Welsh, and
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Categorical relations among matroids, fuzzy matroids and fuzzifying matroids
2010Summary: The aim of this paper is to study the categorical relations between matroids. Goetschel-Voxman's fuzzy matroids and Sin's fuzzifying matroids. It is shown that the category of fuzzifying matroids is isomorphic to that of closed fuzzy matroids and the latter is concretely coreflective in the category of fuzzy matroids.
Lu, Ling-Xia, Zheng, Wei-Wei
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Advances in Applied Mathematics, 2022
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James G. Oxley, Simon Pfeil
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James G. Oxley, Simon Pfeil
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Combinatorica, 1981
This paper exploits and extends results of Edmonds, Cunningham, Cruse and McDiarmid on matroid intersections. Letr 1 andr 2 be rank functions of two matroids defined on the same setE. For everyS ⊂E, letr 12(S) be the largest cardinality of a subset ofS independent in both matroids, 0≦k≦r 12(E)−1. It is shown that, ifc is nonnegative and integral, there
Heinz Gröflin, Alan J. Hoffman
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This paper exploits and extends results of Edmonds, Cunningham, Cruse and McDiarmid on matroid intersections. Letr 1 andr 2 be rank functions of two matroids defined on the same setE. For everyS ⊂E, letr 12(S) be the largest cardinality of a subset ofS independent in both matroids, 0≦k≦r 12(E)−1. It is shown that, ifc is nonnegative and integral, there
Heinz Gröflin, Alan J. Hoffman
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Connectivity of cycle matroids and bicircular matroids
Ars Comb., 1999A unified approach is presented to prove former connectivity results of Tutte, Cunningham, Inukai and Weinberg, Oxley and Wagner.
Chen, Zhi-Hong +2 more
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Canadian Mathematical Bulletin, 1967
In this note we study dependence in matroids as an exercise in combinational algebra. Because the work seems to have little connection with graph theory we will not use Tutte′s approach (1) which uses dual concepts. To define a matroid we use Edmunds (2).
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In this note we study dependence in matroids as an exercise in combinational algebra. Because the work seems to have little connection with graph theory we will not use Tutte′s approach (1) which uses dual concepts. To define a matroid we use Edmunds (2).
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Annals of Combinatorics, 2000
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On Specializations of Matroids
Studies in Applied Mathematics, 1980In this paper, we give an internal description of a weak map between two matroids on the same set. This description is similar to the description of an elementary strong map in terms of a modular cut.
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