Results 51 to 60 of about 4,000 (161)
Binary supersolvable matroids and modular constructions [PDF]
Proceedings of the American Mathematical Society, 1991 A matroid is supersolvable if its lattice of flats contains a maximal chain of modular elements. \textit{R. P. Stanley} [Algebra Univers. 2, 197- 217 (1972; Zbl 0256.06002)] proved that the cycle matroid \(M(G)\) of a graph \(G\) is supersolvable if and only if \(G\) is chordal. The main result of this paper extends Stanley's theorem by showing that if
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Naval Research Logistics (NRL), Volume 72, Issue 1, Page 133-147, February 2025.Abstract A classic result of Korte and Hausmann [1978] and Jenkyns [1976] bounds the quality of the greedy solution to the problem of finding a maximum value basis of an independence system (E,ℐ)$$ \left(E,\mathcal{I}\right) $$ in terms of the rank‐quotient. We extend this result in two ways.
Sven de Vries +2 more
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An introduction to coding sequences of graphs
, 2016 In his pioneering paper on matroids in 1935, Whitney obtained a characterization for binary matroids and left a comment at end of the paper that the problem of characterizing graphic matroids is the same as that of characterizing matroids which ...
Ghosh, Shamik +2 more
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A flow‐based ascending auction to compute buyer‐optimal Walrasian prices
Networks, Volume 84, Issue 2, Page 161-180, September 2024.Abstract We consider a market where a set of objects is sold to a set of buyers, each equipped with a valuation function for the objects. The goal of the auctioneer is to determine reasonable prices together with a stable allocation. One definition of “reasonable” and “stable” is a Walrasian equilibrium, which is a tuple consisting of a price vector ...
Katharina Eickhoff +4 more
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Valuative invariants for large classes of matroids
Journal of the London Mathematical Society, Volume 110, Issue 3, September 2024.Abstract We study an operation in matroid theory that allows one to transition a given matroid into another with more bases via relaxing a stressed subset. This framework provides a new combinatorial characterization of the class of (elementary) split matroids.
Luis Ferroni, Benjamin Schröter
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The Cocycle Lattice of Binary Matroids
European Journal of Combinatorics, 1993 If the weight of every cut in an edge-weighted simple graph is an integer, then the weight of every edge is an integer or a half-integer. This property \(P\) does not generalize to all binary matroids (but it does if the matroid has no parallel elements or Fano minors). The authors study the lattice (grid) generated by the incidence vectors of cocycles
Lovász, László, Seress, Ákos
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Binary matroids that classify forests
Algebra and Discrete Mathematics, 2022 Elementary arguments show that a tree or forest is determined (up to isomorphism) by binary matroids defined using the adjacency matrix.
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A notion of minor-based matroid connectivity
, 2018 For a matroid $N$, a matroid $M$ is $N$-connected if every two elements of $M$ are in an $N$-minor together. Thus a matroid is connected if and only if it is $U_{1,2}$-connected.
Gershkoff, Zachary, Oxley, James
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The Asymptotic Number of Binary Codes and Binary Matroids [PDF]
SIAM Journal on Discrete Mathematics, 2005 12 ...
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On the impossibility of decomposing binary matroids
Operations Research Letters, 2022 We show that there exist $k$-colorable matroids that are not $(b,c)$-decomposable when $b$ and $c$ are constants. A matroid is $(b,c)$-decomposable, if its ground set of elements can be partitioned into sets $X_1, X_2, \ldots, X_l$ with the following two properties. Each set $X_i$ has size at most $ck$. Moreover, for all sets $Y$ such that $|Y \cap X_i|
Marilena Leichter +2 more
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