Results 11 to 20 of about 155 (58)
Defining bicircular matroids in monadic logic [PDF]
, 2020 We conjecture that the class of frame matroids can be characterised by a sentence in the monadic second-order logic of matroids, and we prove that there is such a characterisation for the class of bicircular matroids.
Funk, Daryl +2 more
core +3 more sources
The Tutte Polynomial of Some Matroids
International Journal of Combinatorics, Volume 2012, Issue 1, 2012., 2012 The Tutte polynomial of a graph or a matroid, named after W. T. Tutte, has the important universal property that essentially any multiplicative graph or network invariant with a deletion and contraction reduction must be an evaluation of it. The deletion and contraction operations are natural reductions for many network models arising from a wide range
Criel Merino +3 more
wiley +1 more source
Excluded minors for the class of split matroids [PDF]
, 2018 The class of split matroids arises by putting conditions on the system of split hyperplanes of the matroid base polytope. It can alternatively be defined in terms of structural properties of the matroid.
Cameron, Amanda, Mayhew, Dillon
core +3 more sources
Excluded minors are almost fragile [PDF]
, 2020 Let M be an excluded minor for the class of P-representable matroids for some partial field P, and let N be a 3-connected strong P-stabilizer that is non-binary.
Brettell, Nick +4 more
core +4 more sources
Excluded minors are almost fragile II: essential elements
, 2023 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 ...
Brettell, Nick +3 more
core +1 more source
On perturbations of highly connected dyadic matroids [PDF]
, 2018 Geelen, Gerards, and Whittle [3] announced the following result: let $q = p^k$ be a prime power, and let $\mathcal{M}$ be a proper minor-closed class of $\mathrm{GF}(q)$-representable matroids, which does not contain $\mathrm{PG}(r-1,p)$ for sufficiently
Grace, Kevin, van Zwam, Stefan H. M.
core +3 more sources
Extremal Problems in Matroid Connectivity [PDF]
, 2014 Matroid k-connectivity is typically defined in terms of a connectivity function. We can also say that a matroid is 2-connected if and only if for each pair of elements, there is a circuit containing both elements.
Moss, John Tyler
core +2 more sources
Internally 4-Connected Binary Matroids with Every Element in Three Triangles [PDF]
, 2019 Let M be an internally 4-connected binary matroid with every element in exactly three triangles. Then M has at least four elements e such that si(M/e) is internally 4-connected.
Chun, Carolyn, Oxley, James
core +2 more sources
Non-separating cocircuits in binary matroids
Linear Algebra and its Applications, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +1 more source
Towards a splitter theorem for internally 4-connected binary matroids IX: The theorem [PDF]
, 2016 Let M be a binary matroid that is internally 4-connected, that is, M is 3-connected, and one side of every 3-separation is a triangle or a triad. Let N be an internally 4-connected proper minor of M.
Chun, Carolyn +2 more
core +2 more sources