7 papers
Testing the max-flow min-cut property and the replication conjecture
Ahmad Abdi, Tamás Schwarcz
The replication conjecture [Conforti and Cornuéjols, 1993] states that every clutter with the packing property has the MFMC property. If true, this conjecture would have far-reach…
Generalizing the Multiple Exchange Property for Matroid Bases
Taihei Oki, Tamás Schwarcz
The multiple exchange property for matroid bases states that for any bases and of a matroid and any subset , there exists a subset $Y\subseteq B\se…
Fixed-parameter tractability and hardness for Steiner rooted and locally connected orientations
Kristóf Bérczi, Florian Hörsch, András Imolay +1
Finding a Steiner strongly -arc-connected orientation is particularly relevant in network design and reliability, as it guarantees robust communication between a designated set…
Interaction between skew-representability, tensor products, extension properties, and rank inequalities
Kristóf Bérczi, Boglárka Gehér, András Imolay +3
Skew-representable matroids form a fundamental class in matroid theory, bridging combinatorics and linear algebra. They play an important role in areas such as coding theory, optim…
Matroid products via submodular coupling
Kristóf Bérczi, Boglárka Gehér, András Imolay +3
The study of matroid products traces back to the 1970s, when Lovász and Mason studied the existence of various types of matroid products with different strengths. Among these, the…
Towards the Proximity Conjecture on Group-Labeled Matroids
Dániel Garamvölgyi, Ryuhei Mizutani, Taihei Oki +2
Consider a matroid whose ground set is equipped with a labeling to an abelian group. A basis of is called -avoiding if the sum of the labels of its elements is not in a…