Zobrazeno 31 - 40
of 535
pro vyhledávání: '"Oxley, James"'
Autor:
Fife, Tara, Oxley, James
Nested matroids were introduced by Crapo in 1965 and have appeared frequently in the literature since then. A flat of a matroid $M$ is Hamiltonian if it has a spanning circuit. A matroid $M$ is nested if and only if its Hamiltonian flats form a chain
Externí odkaz:
http://arxiv.org/abs/1801.06882
Autor:
Oxley, James, Pfeil, Simon
Publikováno v:
In Advances in Applied Mathematics October 2022 141
Publikováno v:
In Journal of Combinatorial Theory, Series B January 2022 152:80-120
Seymour's Splitter Theorem is a basic inductive tool for dealing with $3$-connected matroids. This paper proves a generalization of that theorem for the class of $2$-polymatroids. Such structures include matroids, and they model both sets of points a
Externí odkaz:
http://arxiv.org/abs/1706.08027
Autor:
Gershkoff, Zachary, Oxley, James
Publikováno v:
Advances in Applied Mathematics Volume 100, September 2018, Pages 163-178
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. This paper proves that $U_{1,2}$ is the only connected matroid $N$ such
Externí odkaz:
http://arxiv.org/abs/1705.03418
We consider the GF$(4)$-representable matroids with a circuit-hyperplane such that the matroid obtained by relaxing the circuit-hyperplane is also GF$(4)$-representable. We characterize the structure of these matroids as an application of structure t
Externí odkaz:
http://arxiv.org/abs/1704.07306
Akademický článek
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Autor:
Chun, Carolyn, Oxley, James
Let $M$ be an internally $4$-connected binary matroid with every element in three triangles. Then $M$ has at least four elements $e$ such that si$(M/e)$ is internally 4-connected.
Comment: 14 pages, 1 figure
Comment: 14 pages, 1 figure
Externí odkaz:
http://arxiv.org/abs/1608.06013
Autor:
Chun, Carolyn, Oxley, James
Let $M$ be a $3$-connected binary matroid; $M$ is internally $4$-connected if one side of every $3$-separation is a triangle or a triad, and $M$ is $(4,4,S)$-connected if one side of every $3$-separation is a triangle, a triad, or a $4$-element fan.
Externí odkaz:
http://arxiv.org/abs/1608.01027
Autor:
Fife, Tara, Oxley, James
A laminar family is a collection $\mathscr{A}$ of subsets of a set $E$ such that, for any two intersecting sets, one is contained in the other. For a capacity function $c$ on $\mathscr{A}$, let $\mathscr{I}$ be $\{I:|I\cap A| \leq c(A)\text{ for all
Externí odkaz:
http://arxiv.org/abs/1606.08354