Results 71 to 80 of about 9,755 (179)

Rough sets and matroidal contraction [PDF]

, 2012
Rough sets are efficient for data pre-processing in data mining. As a generalization of the linear independence in vector spaces, matroids provide well-established platforms for greedy algorithms.
Wang, Jingqian, Zhu, William
core  

A decomposition theory for matroids. VI. Almost regular matroids

Journal of Combinatorial Theory, Series B, 1992
This paper introduces the class of almost regular matroids. These are the binary matroids \(M\) for which there is a partition (del, con) of \(E(M)\) into non-empty sets such that (i) \(M\backslash e\) is regular if \(e\) is in del; (ii) \(M/e\) is regular if \(e\) is in con; and (iii) every circuit contains an even number of members of con while every
openaire   +1 more source

Basilica: New canonical decomposition in matching theory

Journal of Graph Theory, Volume 108, Issue 3, Page 508-542, March 2025.
Abstract In matching theory, one of the most fundamental and classical branches of combinatorics, canonical decompositions of graphs are powerful and versatile tools that form the basis of this theory. However, the abilities of the known canonical decompositions, that is, the Dulmage–Mendelsohn, Kotzig–Lovász, and Gallai–Edmonds decompositions, are ...
Nanao Kita
wiley   +1 more source

On inner independence systems

Naval Research Logistics (NRL), Volume 72, Issue 1, Page 133-147, February 2025.
Abstract A classic result of Korte and Hausmann [1978] and Jenkyns [1976] bounds the quality of the greedy solution to the problem of finding a maximum value basis of an independence system (E,ℐ)$$ \left(E,\mathcal{I}\right) $$ in terms of the rank‐quotient. We extend this result in two ways.
Sven de Vries, Stephen Raach, Rakesh V. Vohra   +2 more
wiley   +1 more source

Matroid Theory and Supergravity

, 1998
8 pages, Revtex, to appear in Rev. Mex.
openaire   +3 more sources

The category of a partitioned fan

Journal of the London Mathematical Society, Volume 111, Issue 2, February 2025.
Abstract In this paper the notion of an admissible partition of a simplicial polyhedral fan is introduced and the category of a partitioned fan is defined as a generalisation of the τ$\tau$‐cluster morphism category of a finite‐dimensional algebra. This establishes a complete lattice of categories around the τ$\tau$‐cluster morphism category, which is ...
Maximilian Kaipel
wiley   +1 more source

Network theory and transversal matroids

Discrete Applied Mathematics, 1980
AbstractVarious matroidal models for the solvability of active linear networks are described in a unified way and compared with one another. One of the conclusions is that different authors used the concept of “generality” in different ways and their methods are not equivalent. Another conclusion is that some of the seemingly equivalent data structures
Recski, András, Iri, Masao
openaire   +2 more sources

Dense circuit graphs and the planar Turán number of a cycle

Journal of Graph Theory, Volume 108, Issue 1, Page 27-38, January 2025.
Abstract The planar Turán number ex P ( n , H ) of a graph H is the maximum number of edges in an n‐vertex planar graph without H as a subgraph. Let C k denote the cycle of length k. The planar Turán number ex P ( n , C k ) is known for k ≤ 7. We show that dense planar graphs with a certain connectivity property (known as circuit graphs) contain large ...
Ruilin Shi, Zach Walsh, Xingxing Yu
wiley   +1 more source

Analyzing single-valued neutrosophic fuzzy graphs through matroid perspectives

Ain Shams Engineering Journal
We hope to present this paper on the emergence of a novel category of matroids derived from single-valued neutrosophic (SVN) fuzzy-graphs. The findings of this study make a substantial contribution to both matroid theory and the field of neutrosophic ...
S.M. Balaji, D. Meiyappan, R. Sujatha
doaj   +1 more source

Correlation bounds for fields and matroids

, 2018
Let $G$ be a finite connected graph, and let $T$ be a spanning tree of $G$ chosen uniformly at random. The work of Kirchhoff on electrical networks can be used to show that the events $e_1 \in T$ and $e_2 \in T$ are negatively correlated for any distinct
Huh, June, Schröter, Benjamin, Wang, Botong   +2 more
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