Binary matroid

In matroid theory, a binary matroid is a matroid that can be represented over the finite field GF(2). That is, up to isomorphism, they are the…

Papers overview

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2019

The critical threshold of a (simple binary) matroid N is the infimum over all ρ such that any N-free matroid M with |M | > ρ2 has…

2018

Given an $n$-connected binary matroid, we obtain a necessary and sufficient condition for its single-element coextensions to be…

2017

The isotropic matroid M [IAS(G)] of a graph G is a binary matroid, which is equivalent to the isotropic system introduced by…

2016

For each integer $n \geq 2$, we prove that, if $M$ is a simple rank-$r$ $PG(n-1,2)$-free binary matroid with $|M|>\left(1-\frac{3…

2016

This thesis is motivated by the following question: how many elements can a simple binary matroid with no PG(t, 2)-minor have…

2015

We prove, by means of an exact structural description, that every simple triangle-free binary matroid $M$ with $|M| > \tfrac{33…

2012

An excluded minor characterization for the class of binary signed-graphic matroids with graphic cocircuits is provided. In this…

2012

The weak-map order on the matroid base polytopes is the partial order defined by inclusion. Lucas proved that the base polytope…

2009

The property of the circuit modular pair and the application of it to describe the characteristic of binary matroid are studied…

2006

Further work of Brylawski and Heron (see [4, p. 315]) explores other characterizations of Eulerian binary matroids. They showed…