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...pendent sets are all subsets of ''E''. It is a special case of a [[uniform matroid]].<ref>{{cite book | title = Matroid Theory ...

...a [[vector space]], or the number of elements of a [[matroid]] minus its [[Matroid rank|rank]].<ref>{{cite book |last1=Loebl |first1=Martin |last2=Nešetřil |f == Matroid == ...

In mathematics, a '''bipartite matroid''' is a [[matroid]] all of whose circuits have [[even number|even]] size. ...nd only if <math>r</math> is an odd number, because the circuits in such a matroid have size <math>r+1</math>. ...

...air of elements belongs to a three-element circuit (a ''triangle'') of the matroid.<ref name="m69">{{citation | title = Matroid Theory ...

...t <math>E</math> and <math>F</math> have the same cardinality. For a delta-matroid, either of the two elements may belong to either of the two sets, and it is ...when the [[convex hull]] of its [[indicator vector]]s (the analogue of a [[matroid polytope]]) has the property that every edge length is either one or the [[ ...

{{Short description|Matroid in which every permutation is a symmetry}} In mathematics, a '''uniform matroid''' is a [[matroid]] in which the independent sets are exactly the sets containing at most ''r ...

...atroid|matroid theory]], a '''binary matroid''' is a matroid that can be [[Matroid representation|represented]] over the [[finite field]] [[GF(2)]].<ref name= | title = Matroid Theory ...

...ructed via the bases of a [[matroid]]. Given a matroid <math>M</math>, the matroid polytope <math>P_M</math> is the [[convex hull]] of the [[indicator vector] Let <math>M</math> be a [[matroid]] on <math>n</math> elements. Given a basis <math>B \subseteq \{1,\dots, n\ ...

{{Short description|Matroid with complemented basis sets}} In [[matroid theory]], the '''dual''' of a matroid <math>M</math> is another matroid <math>M^\ast</math> that has the same elements as <math>M</math>, and in wh ...

{{Short description|Join-meet algebra on matroid flats}} ...nd infinite, matroids, and every geometric or matroid lattice comes from a matroid in this way. ...

...titional matroid''' is a [[matroid]] that is a [[direct sum]] of [[uniform matroid]]s.<ref>{{citation ...f allowed elements from this category. The independent sets of a partition matroid are exactly the sets in which, for each category, the number of elements fr ...

In [[matroid theory]], an '''Eulerian matroid''' is a matroid whose elements can be partitioned into a collection of disjoint circuits. ...ts are the sets of exactly <math>r+1</math> elements. Therefore, a uniform matroid is Eulerian if and only if <math>r+1</math> is a divisor of <math>n</math>. ...

...parameter tractable]] for linear matroids when parameterized both by the [[matroid rank]] and the field size of a linear representation. ...ning the length of the shortest cycle in a graph: the girth of a [[graphic matroid]] is the same as the girth of its underlying graph.<ref name="ccd">{{citati ...

{{Short description|Matroid without short circuits}} [[File:Vamos matroid.svg|thumb|The [[Vámos matroid]], a paving matroid of rank four; the shaded parallelograms depict its five circuits of size fo ...

{{Short description|Matroid with no linear representation}} [[File:Vamos matroid.svg|thumb|The Vámos matroid; the shaded parallelograms depict its five circuits of size four]] ...

...wing additional property, related to the [[Basis of a matroid|bases of the matroid]].<ref name=":0">{{Cite journal|date=2016-01-01|title=An infinite family of ...04140X|issn=1755-1633|doi-access=free}}</ref> A '''strongly-base-orderable matroid''' has the following stronger property:<blockquote>For any two bases <math> ...

...ph theory)|vertices]] that can be reached by vertex-disjoint [[Path (graph theory)|paths]] in a [[directed graph]]. The concept of a gammoid was introduced and shown to be a matroid by {{harvs|first=Hazel|last=Perfect|authorlink=Hazel Perfect|year=1968|txt} ...

...n matroid sums, and to compute the largest common independent set in the [[matroid intersection|intersection]] of two given matroids.<ref name="fgt">{{citatio | contribution = 5. Fractional arboricity and matroid methods ...

{{short description|Maximal independent set of the matroid}} ...matics, a '''basis''' of a [[matroid]] is a maximal independent set of the matroid—that is, an independent set that is not contained in any other independent ...

...roid representation|represented]] over that field has only finitely many [[matroid minor|excluded minors]].<ref>{{citation | contribution = Combinatorial theory, old and new ...