On the Packing/Covering Conjecture of Infinite Matroids
Attila Jo\'o

TL;DR
This paper proves a special case of the Packing/Covering Conjecture for countable matroids that are either finitary or cofinitary, linking it to matroid intersection problems and extending known results.
Contribution
It establishes the conjecture for countable, well-behaved matroids with finitary or cofinitary components, connecting packing/covering to matroid intersection theory.
Findings
Proves the conjecture for countable finitary or cofinitary matroids.
Links packing/covering conjecture to matroid intersection problems.
Shows the generalized Nash-Williams' Conjecture holds for these matroids.
Abstract
The Packing/Covering Conjecture was introduced by Bowler and Carmesin motivated by the Matroid Partition Theorem by Edmonds and Fulkerson. A packing for a family of matroids on the common edge set is a system of pairwise disjoint subsets of where is panning in . Similarly, a covering is a system with where is independent in . The conjecture states that for every matroid family on there is a partition such that admits a packing and admits a covering. We prove the special case where is countable and each is either finitary or cofinitary. The connection between packing/covering and matroid intersection problems discovered by Bowler and Carmesin…
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Taxonomy
TopicsAdvanced Graph Theory Research · Advanced Topology and Set Theory · Limits and Structures in Graph Theory
