Results 1 to 10 of about 4,003 (147)
Generalized Index Coding Problem and Discrete Polymatroids [PDF]
Entropy, 2020 The connections between index coding and matroid theory have been well studied in the recent past. Index coding solutions were first connected to multi linear representation of matroids.
Anoop Thomas, Balaji Sundar Rajan
doaj +2 more sources
Templates for Binary Matroids [PDF]
SIAM Journal on Discrete Mathematics, 2017 A binary frame template is a device for creating binary matroids from graphic or cographic matroids. Such matroids are said to conform or coconform to the template. We introduce a preorder on these templates and determine the nontrivial templates that are minimal with respect to this order.
Grace, Kevin, Van Zwam, Stefan H.M.
openaire +7 more sources
Binary matroids and local complementation [PDF]
European Journal of Combinatorics, 2014 We introduce a binary matroid M(IAS(G)) associated with a looped simple graph G. M(IAS(G)) classifies G up to local equivalence, and determines the delta-matroid and isotropic system associated with G.
Traldi, Lorenzo
core +3 more sources
On n-connected minors of the es-splitting binary matroids
Electronic Journal of Graph Theory and Applications, 2021 The es-splitting operation on an n-connected binary matroid may not yield an n-connected matroid for (n ≥ 3). In this paper, we show that given an n-connected binary matroid M of rank r, the resulting es-splitting binary matroid has an n-connected minor ...
Prashant Pralhad Malavadkar +2 more
doaj +1 more source
On n-connected splitting matroids
AKCE International Journal of Graphs and Combinatorics, 2019 In general, the splitting operation on a binary matroid M does not preserve the connectivity of M. In this paper, we provide sufficient conditions to preserve n-connectedness of a binary matroid under splitting operation.
Y.M. Borse, Ganesh Mundhe
doaj +2 more sources
Cyclic flats of binary matroids
Advances in Applied Mathematics, 2021 In this paper, first steps are taken towards characterising lattices of cyclic flats $\mathcal{Z}(M)$ that belong to matroids $M$ that can be represented over a prescribed finite field $\mathbb{F}_q$. Two natural maps from $\mathcal{Z}(M)$ to the lattice of cyclic flats of a minor of $M$ are given. Binary matroids are characterised via their lattice of
Grezet, Matthias +4 more
openaire +4 more sources
On the cogirth of binary matroids
Advances in Applied Mathematics, 2023 8 ...
Crenshaw, Cameron, Oxley, James
openaire +2 more sources
Minor-closed classes of binary functions [PDF]
Discrete Mathematics & Theoretical Computer ScienceBinary functions are a generalisation of the cocircuit spaces of binary matroids to arbitrary functions. Every rank function is assigned a binary function, and the deletion and contraction operations of binary functions generalise matroid deletion and ...
Benjamin R. Jones
doaj +1 more source
AKCE International Journal of Graphs and Combinatorics, 2020 Spikes are an important class of 3-connected matroids. For an integer , there is a unique binary r-spike denoted by Zr. When a circuit-hyperplane of Zr is relaxed, we obtain another spike and repeating this procedure will produce other non-binary spikes.
Vahid Ghorbani +2 more
doaj +1 more source
Eulerian and Bipartite Binary Delta-matroids
Acta Mathematicae Applicatae Sinica, English Series, 2022 13 pages, 0 figures.
Yan, Qi, Jin, Xian-an
openaire +3 more sources