Results 1 to 10 of about 155 (58)
Matroid connectivity and singularities of configuration hypersurfaces. [PDF]
Lett Math Phys, 2021 Consider a linear realization of a matroid over a field. One associates with it a configuration polynomial and a symmetric bilinear form with linear homogeneous coefficients.
Denham G, Schulze M, Walther U.
europepmc +2 more sources
Contracting an element from a cocircuit [PDF]
Advances in Applied Mathematics, 2008 For the abstract of this paper, please see the PDF ...
Hall, R, Mayhew, D
core +6 more sources
Geometric bijections between spanning subgraphs and orientations of a graph
Journal of the London Mathematical Society, Volume 108, Issue 3, Page 1082-1120, September 2023., 2023 Abstract Let G$G$ be a connected finite graph. Backman, Baker, and Yuen have constructed a family of explicit and easy‐to‐describe bijections between spanning trees of G$G$ and (σ,σ∗)$(\sigma ,\sigma ^*)$‐compatible orientations, where the (σ,σ∗)$(\sigma ,\sigma ^*)$‐compatible orientations are the representatives of equivalence classes of orientations
Changxin Ding
wiley +1 more source
On generalisations of the Aharoni–Pouzet base exchange theorem
Bulletin of the London Mathematical Society, Volume 55, Issue 3, Page 1540-1549, June 2023., 2023 Abstract The Greene–Magnanti theorem states that if M$ M$ is a finite matroid, B0$ B_0$ and B1$ B_1$ are bases and B0=⋃i=1nXi$ B_0=\bigcup _{i=1}^{n} X_i$ is a partition, then there is a partition B1=⋃i=1nYi$ B_1=\bigcup _{i=1}^{n}Y_i$ such that (B0∖Xi)∪Yi$ (B_0 \setminus X_i) \cup Y_i$ is a base for every i$ i$. The special case where each Xi$ X_i$ is
Zsuzsanna Jankó, Attila Joó
wiley +1 more source
Non-separating cocircuits in matroids
Electronic Notes in Discrete Mathematics, 2005 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lemos, Manoel, Melo, T.R.B.
openaire +1 more source
On Density-Critical Matroids [PDF]
, 2019 For a matroid $M$ having $m$ rank-one flats, the density $d(M)$ is $\tfrac{m}{r(M)}$ unless $m = 0$, in which case $d(M)= 0$. A matroid is density-critical if all of its proper minors of non-zero rank have lower density.
Campbell, Rutger +3 more
core +3 more sources
Connectivity of Matroids and Polymatroids [PDF]
, 2021 This dissertation is a collection of work on matroid and polymatroid connectivity. Connectivity is a useful property of matroids that allows a matroid to be decomposed naturally into its connected components, which are like blocks in a graph.
Gershkoff, Zachary R
core +2 more sources
The structure of 3-connected matroids of path-width three [PDF]
, 2003 A 3-connected matroid M is sequential or has path width 3 if its ground set E(M) has a sequential ordering, that is, an ordering (e₁,e₂,...,en) such that ({e₁,e₂,...,ek},{ek+1,ek+2,...,en}) is a 3-separation for all k in {3,4,...,n-3}.
Hall, R., Oxley, J., Semple, C.
core +1 more source
Characterizations of Certain Classes of Graphs and Matroids [PDF]
, 2022 ``If a theorem about graphs can be expressed in terms of edges and cycles only, it probably exemplifies a more general theorem about matroids. Most of my work draws inspiration from this assertion, made by Tutte in 1979.
Singh, Jagdeep
core +2 more sources
COMs: Complexes of Oriented Matroids [PDF]
, 2017 In his seminal 1983 paper, Jim Lawrence introduced lopsided sets and featured them as asymmetric counterparts of oriented matroids, both sharing the key property of strong elimination.
Bandelt, Hans-Juergen +2 more
core +3 more sources