Graph theory | Matroid theory

Bicircular matroid

In the mathematical subject of matroid theory, the bicircular matroid of a graph G is the matroid B(G) whose points are the edges of G and whose independent sets are the edge sets of pseudoforests of G, that is, the edge sets in which each connected component contains at most one cycle. The bicircular matroid was introduced by and explored further by and others. It is a special case of the frame matroid of a biased graph. (Wikipedia).

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Kevin Hendrey - Obstructions to bounded branch-depth in matroids (CMSA Combinatorics Seminar)

Kevin Hendrey (Institute for Basic Science) presents โ€œObstructions to bounded branch-depth in matroidsโ€, 24 November 2020 (CMSA Combinatorics Seminar).

From playlist CMSA Combinatorics Seminar

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Using a set of points determine if the figure is a parallelogram using the midpoint formula

๐Ÿ‘‰ Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr

From playlist Quadrilaterals on a Coordinate Plane

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Determining if a set of points makes a parallelogram or not

๐Ÿ‘‰ Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr

From playlist Quadrilaterals on a Coordinate Plane

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Using the slope formula to determine if points make up a rectangle

๐Ÿ‘‰ Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr

From playlist Quadrilaterals on a Coordinate Plane

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Determine if a set of points is a parallelogram by using the slope formula

๐Ÿ‘‰ Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr

From playlist Quadrilaterals on a Coordinate Plane

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How to determine the perimeter of a quadrilateral using distance formula of four points

๐Ÿ‘‰ Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr

From playlist Quadrilaterals on a Coordinate Plane

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Determine if a set of points is a parallelogram using the distance formula

๐Ÿ‘‰ Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr

From playlist Quadrilaterals on a Coordinate Plane

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Determine if a set of points is a trapezoid or not

๐Ÿ‘‰ Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr

From playlist Quadrilaterals on a Coordinate Plane

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Determine if a set of points makes up a rectangle using the distance formula

๐Ÿ‘‰ Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr

From playlist Quadrilaterals on a Coordinate Plane

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Joseph Bonin: Delta-matroids as subsystems of sequences of Higgs lifts

Abstract: Delta-matroids generalize matroids. In a delta-matroid, the counterparts of bases, which are called feasible sets, can have different sizes, but they satisfy a similar exchange property in which symmetric differences replace set differences. One way to get a delta-matroid is to t

From playlist Combinatorics

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Nonlinear algebra, Lecture 13: "Polytopes and Matroids ", by Mateusz Michalek

This is the thirteenth lecture in the IMPRS Ringvorlesung, the advanced graduate course at the Max Planck Institute for Mathematics in the Sciences.

From playlist IMPRS Ringvorlesung - Introduction to Nonlinear Algebra

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Yusuke Kobayashi: A weighted linear matroid parity algorithm

The lecture was held within the framework of the follow-up workshop to the Hausdorff Trimester Program: Combinatorial Optimization. Abstract: The matroid parity (or matroid matching) problem, introduced as a common generalization of matching and matroid intersection problems, is so gener

From playlist Follow-Up-Workshop "Combinatorial Optimization"

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Victor Chepoi: Simple connectivity, local to global, and matroids

Victor Chepoi: Simple connectivity, local-to-global, and matroids A basis graph of a matroid M is the graph G(M) having the bases of M as the vertex-set and the pairs of bases differing by an elementary exchange as edges. Basis graphs of matroids have been characterized by S.B. Maurer, J.

From playlist HIM Lectures 2015

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Anna De Mier: Approximating clutters with matroids

Abstract: There are several clutters (antichains of sets) that can be associated with a matroid, as the clutter of circuits, the clutter of bases or the clutter of hyperplanes. We study the following question: given an arbitrary clutter ฮ›, which are the matroidal clutters that are closest

From playlist Combinatorics

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Gyula Pap: Linear matroid matching in the oracle model

Gyula Pap: Linear matroid matching in the oracle model Linear matroid matching is understood as a special case of matroid matching when the matroid is given with a matrix representation. However, for certain examples of linear matroids, the matrix representation is not given, and actuall

From playlist HIM Lectures 2015

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Zoltรกn Szigeti: Packing of arborescences with matroid constraints via matroid intersection

The lecture was held within the framework of the follow-up workshop to the Hausdorff Trimester Program: Combinatorial Optimization. Abstract: Edmonds characterized digraphs having a packing of k spanning arborescences in terms of connectivity and later in terms of matroid intersection. D

From playlist Follow-Up-Workshop "Combinatorial Optimization"

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Sahil Singla: Online Matroid Intersection Beating Half for Random Arrival

We study a variant of the online bipartite matching problem that we call the online matroid intersection problem. For two matroids M1 and M2 defined on the same ground set E, the problem is to design an algorithm that constructs the largest common independent set in an online fashion. At e

From playlist HIM Lectures 2015

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Determining if a set of points is a rhombus, square or rectangle

๐Ÿ‘‰ Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr

From playlist Quadrilaterals on a Coordinate Plane

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How to determine if a set of points makes up a rectangle using the distance formula

๐Ÿ‘‰ Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr

From playlist Quadrilaterals on a Coordinate Plane

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The log-concavity conjecture and the tropical Laplacian - June Huh

June Huh Princeton University; Veblen Fellow, School of Mathematics February 17, 2015 The log-concavity conjecture predicts that the coefficients of the chromatic (characteristic) polynomial of a matroid form a log-concave sequence. The known proof for realizable matroids uses algebraic g

From playlist Mathematics

Related pages

Geometric lattice | Graph (discrete mathematics) | Finite field | Glossary of graph theory | Graphic matroid | Multigraph | Pseudoforest | Matroid | Tree (graph theory) | Graph theory | Induced subgraph | Mathematics | Gain graph | Field (mathematics) | Circuit rank | Cycle (graph theory) | Family of sets | Biased graph | Matroid representation | Matroid minor | Journal of Combinatorial Theory | Regular matroid