Results 51 to 60 of about 22,632 (241)
A weighted linear matroid parity algorithm [PDF]
Symposium on the Theory of Computing, 2017 The matroid parity (or matroid matching) problem, introduced as a common generalization of matching and matroid intersection problems, is so general that it requires an exponential number of oracle calls.
S. Iwata, Yusuke Kobayashi
semanticscholar +1 more source
Representing Matroids over the Reals is $\exists \mathbb R$-complete [PDF]
Discrete Mathematics & Theoretical Computer ScienceA matroid $M$ is an ordered pair $(E,I)$, where $E$ is a finite set called the ground set and a collection $I\subset 2^{E}$ called the independent sets which satisfy the conditions: (i) $\emptyset \in I$, (ii) $I'\subset I \in I$ implies $I'\in I$, and ...
Eun Jung Kim +2 more
doaj +1 more source
Reducing the rank of a matroid [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 We consider the rank reduction problem for matroids: Given a matroid $M$ and an integer $k$, find a minimum size subset of elements of $M$ whose removal reduces the rank of $M$ by at least $k$. When $M$ is a graphical matroid this problem is the minimum $
Gwenaël Joret, Adrian Vetta
doaj +1 more source
Algebraic matroids and Frobenius flocks [PDF]
, 2017 We show that each algebraic representation of a matroid $M$ in positive characteristic determines a matroid valuation of $M$, which we have named the {\em Lindstr\"om valuation}.
Bollen, Guus +2 more
core +5 more sources
Gorenstein graphic matroids [PDF]
Israel Journal of Mathematics, 2021 The toric variety of a matroid is projectively normal, and therefore it is Cohen-Macaulay. We provide a complete graph-theoretic classification when the toric variety of a graphic matroid is Gorenstein.
Hibi, T. +4 more
openaire +3 more sources
The Electronic Journal of Combinatorics, 2006 One way to choose a basis of a matroid at random is to choose an ordering of the ground set uniformly at random and then use the greedy algorithm to find a basis. We investigate the class of matroids having the property that this procedure yields a basis uniformly at random.
openaire +2 more sources
Matroid Constrained Fair Allocation Problem
AAAI Conference on Artificial Intelligence, 2019 We consider the problem of allocating a set of indivisible goods among a group of homogeneous agents under matroid constraints and additive valuations, in a fair manner.
Arpita Biswas, Siddharth Barman
semanticscholar +1 more source
On Lattice Path Matroid Polytopes: Integer Points and Ehrhart Polynomial [PDF]
Discrete & Computational Geometry, 2017 In this paper we investigate the number of integer points lying in dilations of lattice path matroid polytopes. We give a characterization of such points as polygonal paths in the diagram of the lattice path matroid.
K. Knauer +2 more
semanticscholar +1 more source
A construction of infinite sets of intertwines for pairs of matroids [PDF]
, 2010 An intertwine of a pair of matroids is a matroid such that it, but none of its proper minors, has minors that are isomorphic to each matroid in the pair.
Bonin, Joseph E.
core +1 more source
Graphic Splitting of Cographic Matroids
Discussiones Mathematicae Graph Theory, 2015 In this paper, we obtain a forbidden minor characterization of a cographic matroid M for which the splitting matroid Mx,y is graphic for every pair x, y of elements of M.
Pirouz Naiyer
doaj +1 more source