Infinite matroid union II

Details Infinite matroid union II Infinite matroid union II

2011-11-02

arxiv.org/abs/1111.0606v1

Mathematics

Combinatorics

24 pages, 4 figures, submitted

Scientific paper

We introduce the \emph{nearly finitary} matroids which form a superclass of the finitary matroids, and prove that the union of two nearly finitary matroids is a matroid and, in fact, nearly finitary. To prove the latter, we appeal to the finitary matroid union theorem established in the first paper of this series. We also characterize the nearly finitary graphic matroids. Using the nearly finitary matroid union result, we establish that the \emph{infinite matroid intersection conjecture} of Nash-Williams is true whenever the first matroid is nearly finitary and the second is the dual of a nearly finitary matroid. From this we derive an alternative matroidal proof of the infinite Menger theorem for locally finite graphs. In addition, we show that the infinite matroid intersection conjecture for finitary implies the general infinite Menger theorem which was conjectured by Erd\H{o}s, and proved only recently by Aharoni and Berger.

Affiliated with

Also associated with

No associations

Rating

Infinite matroid union II does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Infinite matroid union II, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Infinite matroid union II will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-329832