Results 71 to 80 of about 511 (171)
CoRRAn extended abstract of this paper appears in the proceedings of ESA ...
Matthias Bentert +3 more
openaire +3 more sources
Reconfiguring Ordered Bases of a Matroid
CoRR, 2016 For a matroid with an ordered (or "labelled") basis, a basis exchange step removes one element with label $l$ and replaces it by a new element that results in a new basis, and with the new element assigned label $l$. We prove that one labelled basis can be reconfigured to another if and only if for every label, the initial and final elements with that ...
Anna Lubiw, Vinayak Pathak
openaire +2 more sources
An exchange property of matroid
, 1995 Rota's conjecture about n bases in a rank n matroid is solved for n ...
Chan, Wendy
core +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
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 +2 more
wiley +1 more source
On the quasi-transversals of a matroid
, 1995 We show that the set of r-quasi-transversals of a matroid, if nonempty, is the set of bases of a matroid. We also give an alternative proof of the known theorem which identifies the conjugate of the rank partition of a ...
Fonseca, Amélia, Brualdi, Richard A.
core +1 more source
On the Congruency-Constrained Matroid Base
Consider a matroid where all elements are labeled with an element in $\mathbb{Z}$. We are interested in finding a base where the sum of the labels is congruent to $g \pmod m$. We show that this problem can be solved in $\tilde{O}(2^{4m} n r^{5/6})$ time for a matroid with $n$ elements and rank $r$, when $m$ is either the product of two primes or a ...
Siyue Liu, Chao Xu 0002
openaire +2 more sources
A multiply constrained matroid optimization problem
, 1988 We consider the problem of finding a minimum weight basis in a matroid satisfying additional conditions which can be described as follows: each element of the matroid is assigned a colour and feasible bases can use at most a prescribed number of elements
Leclerc, M. +3 more
core +1 more source
, 1973 A matroid may be defined as a collection of sets, called bases, which satisfy a certain exchange axiom. The basis graph of a matroid has a vertex for each basis and an edge for each pair of bases that differ by the exchange of a single pair of elements ...
Maurer, Stephen B
core +1 more source
, 2012 The aim of this paper is to discuss properties of fuzzy regular-flats, fuzzy C- flats, fuzzy alternative-sets and fuzzy i-flats. Moreover, we characterize some peculiar fuzzy matroids via these notions. Finally, we provide a decomposition of fuzzy strong
Talal Ali Al-hawary +1 more
core +1 more source