Results 51 to 60 of about 4,003 (147)
Rough matroids based on coverings [PDF]
, 2013 The introduction of covering-based rough sets has made a substantial contribution to the classical rough sets. However, many vital problems in rough sets, including attribution reduction, are NP-hard and therefore the algorithms for solving them are ...
Yang, Bin, Zhao, Hong, Zhu, William
core
The critical number of dense triangle-free binary matroids
, 2016 We show that, for each real number $\epsilon > 0$ there is an integer $c$ such that, if $M$ is a simple triangle-free binary matroid with $|M| \ge (\tfrac{1}{4} + \epsilon) 2^{r(M)}$, then $M$ has critical number at most $c$.
Geelen, Jim, Nelson, Peter
core +1 more source
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
wiley +1 more source
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
wiley +1 more source
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
openaire +1 more source
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.
openaire +2 more sources
On Local Equivalence, Surface Code States and Matroids
, 2010 Recently, Ji et al disproved the LU-LC conjecture and showed that the local unitary and local Clifford equivalence classes of the stabilizer states are not always the same.
I. Niven +5 more
core +1 more source
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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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
core +1 more source
Circuit Decompositions of Binary Matroids
SIAM Journal on Discrete MathematicsGiven a simple Eulerian binary matroid $M$, what is the minimum number of disjoint circuits necessary to decompose $M$? We prove that $|M| / (\operatorname{rank}(M) + 1)$ many circuits suffice if $M = \mathbb F_2^n \setminus \{0\}$ is the complete binary matroid, for certain values of $n$, and that $\mathcal{O}(2^{\operatorname{rank}(M ...
Bryce Frederickson, Lukas Michel
openaire +2 more sources