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pro vyhledávání: '"Oxley, James"'
Although the unavoidable minors of large 3-connected matroids were found nearly thirty years ago, there has been little progress on solving the corresponding problem for large 4-connected matroids. This paper aims to take a step towards solving that
Externí odkaz:
http://arxiv.org/abs/2405.15207
Autor:
Douthitt, James Dylan, Oxley, James
In 1961, Dirac showed that chordal graphs are exactly the graphs that can be constructed from complete graphs by a sequence of clique-sums. In an earlier paper, by analogy with Dirac's result, we introduced the class of $GF(q)$-chordal matroids as th
Externí odkaz:
http://arxiv.org/abs/2405.02099
The breadth of a tangle $\mathcal{T}$ in a matroid is the size of the largest spanning uniform submatroid of the tangle matroid of $\mathcal{T}$. The matroid $M$ is weakly 4-connected if it is 3-connected and whenever $(X,Y)$ is a partition of $E(M)$
Externí odkaz:
http://arxiv.org/abs/2310.08832
Autor:
Mizell, Matthew, Oxley, James
Targets are matroids that arise from a nested sequence of flats in a projective geometry. This class of matroids was introduced by Nelson and Nomoto, who found the forbidden induced restrictions for binary targets. This paper generalizes their result
Externí odkaz:
http://arxiv.org/abs/2307.02423
Autor:
Crenshaw, Cameron, Oxley, James
Let $G$ be a graph such that, whenever two vertices $x$ and $y$ of $G$ are joined by three internally disjoint paths, $x$ and $y$ are adjacent. Jamison and Mulder determined that the set of such graphs coincides with the set of graphs that can be bui
Externí odkaz:
http://arxiv.org/abs/2306.07386
Autor:
Douthitt, James Dylan, Oxley, James
A graph is chordal if every cycle of length at least four has a chord. In 1961, Dirac characterized chordal graphs as those graphs that can be built from complete graphs by repeated clique-sums. Generalizing this, we consider the class of simple $GF(
Externí odkaz:
http://arxiv.org/abs/2306.07514
Publikováno v:
Journal of Combinatorial Theory, Series B, 163 (2023), 133-218
The class of 2-regular matroids is a natural generalisation of regular and near-regular matroids. We prove an excluded-minor characterisation for the class of 2-regular matroids. The class of 3-regular matroids coincides with the class of matroids re
Externí odkaz:
http://arxiv.org/abs/2206.15188
Publikováno v:
Journal of Combinatorial Theory, Series B, 163 (2023), 272-307
Let $M$ be an excluded minor for the class of $\mathbb{P}$-representable matroids for some partial field $\mathbb{P}$, let $N$ be a $3$-connected strong $\mathbb{P}$-stabilizer that is non-binary, and suppose $M$ has a pair of elements $\{a,b\}$ such
Externí odkaz:
http://arxiv.org/abs/2206.13036
Autor:
Crenshaw, Cameron, Oxley, James
The cycles of a graph give a natural cyclic ordering to their edge-sets, and these orderings are consistent in that two edges are adjacent in one cycle if and only if they are adjacent in every cycle in which they appear together. An orderable matroi
Externí odkaz:
http://arxiv.org/abs/2203.08305