Results 81 to 90 of about 511 (171)
A simple PTAS for weighted matroid matching on strongly base orderable matroids [PDF]
Discrete Applied Mathematics, 2011 8 pages, 3 figures.
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The basis graph of a bicolored matroid
, 2012 Let ϕ be a 2-coloring of the elements of a matroid M. The bicolor basis graph of M is the graph G(B(M),ϕ) with vertex set given by the set of bases of M in which two bases B and B′ are adjacent if B′=(B−e)∪f for some elements e∈B and f∈B′ with ϕ(e)≠ϕ(f).
Eduardo Rivera-Campo +3 more
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Topological properties of activity orders for matroid bases
, 2004 Las Vergnas (European J. Combin. 22 (2001) 709) introduced several lattice structures on the bases of an ordered matroid M by using their external and internal activities.
Bruce E. Sagan +3 more
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Adjacency, Inseparability, and Base Orderability in Matroids
European Journal of Combinatorics, 2000 Two elements in an oriented matroid are inseparable if they have either the same sign in every signed circuit containing them both or opposite signs in every signed circuit containing them both. Two elements of a matroid are adjacent if there is no \({\mathcal M}(K_4)\)-minor using them both, and in which they correspond to a matching of \(K_4\).
Keijsper, J.C.M. +2 more
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CONTRIBUTIONS TO ALGORITHMIC MATROID PROBLEMS
, 2015 In this thesis, we obtain several algorithms for problems related to matroids, a structure that generalizes the concept of linear independence in a vector space and an acyclic subgraph structure in a graph.
Huang, Jinyu
core
On matroids with many common bases
Discrete Mathematics, 1999 Let \({\mathcal B}(M)\) denote the collection of bases of a matroid \(M.\) The author shows that if \(M_1\) and \(M_2\) are connected matroids having the same ground set and the symmetric difference \( {\mathcal B}(M_1)\Delta {\mathcal B}(M_2)\) has cardinality two, then, apart from a trivial exception, \(M_1\) and \(M_2\) are related via the ...
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Tropical Carathéodory with Matroids. [PDF]
Discrete Comput Geom, 2023 Loho G, Sanyal R.
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The dependence graph for bases in matroids
Discrete Mathematics, 1977 AbstractThis paper discusses a certain graph, called the “dependence graph” (“the DPG”), that can be defined naturally for a given independent set in a matroid. We are mainly concerned with the DPG of bases, and we study what the DPG of a base tells about the matroid.
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Matroid connectivity and singularities of configuration hypersurfaces. [PDF]
Lett Math Phys, 2021 Denham G, Schulze M, Walther U.
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