Year: 2026
Type: article
Abstract: The concept of domination has increasingly found powerful extensions within the structural framework of matroid theory. This paper investigates the structural, algebraic, and algorithmic properties of domination in matroids, unifying classical network domination with matroidal invariants such as closures, independent sets, and fundamental circuits. We formalise the notion of a dominating configuration in a general matroid M = (E,I) and analyse the combinatorial parameters governing its minimal representations. Specifically, we characterize the complexity of computing the minimum-weight domination number across prominent matroid classes, including graphic matroids. By leveraging the matroid rank function r(M), we establish novel lower and upper bounds for the domination invariant.
Authors: Jyoti D K, Thukarama V
Institution: Government of Karnataka
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W7223694769