#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:
-------------------------------------+-------------------------------------
Comment (by Rudi):
Replying to [comment:10 tscrim]:
> 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?
No, just that if `M` is binary and `C` is a circuit of `M`, then `x\not\in
C` is a chord of `C` if and only if `x` is spanned by `C`. So from that
perspective, you could define weak chordality in terms of each `C`
spanning an element outside `C`, and ordinary chordality as you did. The
two notions coincide for binary matroids.
I came across this paper by Joe Bonin in which he defines the same weaker
notion of chordality, using slightly different words (def. 7):
http://home.gwu.edu/~jbonin/wheelsweb.pdf
> 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
`^^;;` ).
I'll review it.
--
Ticket URL: <http://trac.sagemath.org/ticket/18484#comment:11>
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.
