Results 31 to 40 of about 4,000 (161)

Connected Hyperplanes in Binary Matroids

Journal of Combinatorial Theory, Series B, 2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
McNulty, Jennifer, Wu, Haidong
openaire   +2 more sources

Matroidal Structure of Rough Sets Based on Serial and Transitive Relations

Journal of Applied Mathematics, 2012
The theory of rough sets is concerned with the lower and upper approximations of objects through a binary relation on a universe. It has been applied to machine learning, knowledge discovery, and data mining. The theory of matroids is a generalization of
Yanfang Liu, William Zhu
doaj   +1 more source

Excluding Kuratowski graphs and their duals from binary matroids

, 2017
We consider some applications of our characterisation of the internally 4-connected binary matroids with no M(K3,3)-minor. We characterise the internally 4-connected binary matroids with no minor in some subset of {M(K3,3),M*(K3,3),M(K5),M*(K5)} that ...
Mayhew, Dillon, Royle, Gordon, Whittle, Geoff   +2 more
core   +1 more source

Canonical Binary $$\Delta $$-Matroids

Graphs and Combinatorics
The handle slide operation, originally defined for ribbon graphs, was extended to delta-matroids by I. Moffatt and E. Mphako-Bandab, who show that, using a delta-matroid analogue of handle slides, every binary delta-matroid in which the empty set is feasible can be written in a canonical form analogous to the canonical form for one-vertex maps on a ...
Avohou, Rémi Cocou, Servatius, Brigitte, Servatius, Herman   +2 more
openaire   +3 more sources

Elementary lift and single element coextension of a binary gammoid

AKCE International Journal of Graphs and Combinatorics
It is known that every binary elementary lift of a binary matroid is a matroid obtained by applying the splitting operation on that matroid. An elementary lift of a binary gammoid need not be a binary gammoid.
Shital Dilip Solanki, Ganesh Mundhe, S. B. Dhotre   +2 more
doaj   +1 more source

Nonlinear Matroid Optimization and Experimental Design [PDF]

, 2007
We study the problem of optimizing nonlinear objective functions over matroids presented by oracles or explicitly. Such functions can be interpreted as the balancing of multi-criteria optimization. We provide a combinatorial polynomial time algorithm for
Eva Riccomagno, Fries A., Henry Wynn, Hugo Maruri-Aguilar, Jon Lee, Robert Weismantel, Shmuel Onn, Yael Berstein   +7 more
core   +7 more sources

Maximum size binary matroids with no AG(3,2)-minor are graphic [PDF]

, 2013
We prove that the maximum size of a simple binary matroid of rank $r \geq 5$ with no AG(3,2)-minor is $\binom{r+1}{2}$ and characterise those matroids achieving this bound.
Kung, Joseph P. S., Mayhew, Dillon, Pivotto, Irene, Royle, Gordon F.   +3 more
core  

Orienting Transversals and Transition Polynomials of Multimatroids

, 2017
Multimatroids generalize matroids, delta-matroids, and isotropic systems, and transition polynomials of multimatroids subsume various polynomials for these latter combinatorial structures, such as the interlace polynomial and the Tutte-Martin polynomial.
Brijder, Robert
core   +1 more source

Adjacency in Binary Matroids

European Journal of Combinatorics, 1986
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

On Some Algorithmic and Structural Results on Flames

Journal of Graph Theory, Volume 110, Issue 4, Page 392-397, December 2025.
ABSTRACT A directed graph F with a root node r is called a flame if for every vertex v other than r the local edge‐connectivity value λ F ( r , v ) from r to v is equal to ϱ F ( v ), the in‐degree of v. It is a classic, simple and beautiful result of Lovász [4] that every digraph D with a root node r has a spanning subgraph F that is a flame and the λ (
Dávid Szeszlér
wiley   +1 more source