#18484: Implement k-chordality of a matroid
-------------------------------------+-------------------------------------
Reporter: Rudi | Owner:
Type: enhancement | Status: needs_review
Priority: minor | Milestone: sage-6.8
Component: matroid theory | Resolution:
Keywords: chord | Merged in:
Authors: Travis Scrimshaw | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
public/matroids/k_chordal-18484 | 6f9e8633781d3843c59d8b89e333b1844c090880
Dependencies: | Stopgaps:
-------------------------------------+-------------------------------------
Changes (by tscrim):
* status: new => needs_review
* commit: => 6f9e8633781d3843c59d8b89e333b1844c090880
* branch: => public/matroids/k_chordal-18484
Old description:
> A matroid is k-chordal if every circuit `C` of size > k has a ''chord'',
> an element `x` of the ground set is a ''chord'' of `C` if there exists `C
> = A \cup B` such that `A \cup x, B \cup x` are circuits.
New description:
A matroid is k-chordal if every circuit `C` of size >= k has a ''chord'',
an element `x` of the ground set is a ''chord'' of `C` if there exists `C
= A \sqcup B` such that `A \cup x, B \cup x` are circuits. Matroids that
are 4-chordal are simply called chordal.
--
Comment:
Hmm...I see why chordality could be a measurement of how close a matroid
is to being binary, but it seems like it needs some extra information
about the flats. From the symmetric difference property, would that imply
that all binary matroids are (4-)chordal? I'm not well versed enough in
matroid theory to answer your question about the existence of a binary
matroid in comment:7. I'm also happy to talk more off-list about about my
interests and learning more matroid theory.
Here's the code and ready for review (only 1 day later than I thought
`^^;;` ).
----
New commits:
||[http://git.sagemath.org/sage.git/commit/?id=6f9e8633781d3843c59d8b89e333b1844c090880
6f9e863]||{{{Implemented checks for matroid chordality.}}}||
--
Ticket URL: <http://trac.sagemath.org/ticket/18484#comment:10>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/d/optout.
