#18484: Implement k-chordality of a matroid
------------------------------------+------------------------
Reporter: Rudi | Owner:
Type: enhancement | Status: new
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:
Dependencies: | Stopgaps:
------------------------------------+------------------------
Comment (by Rudi):
Replying to [comment:8 tscrim]:
> I'm not sure about the relation with binary matroids. Let me think on
that.
That relation is suggested by having the exact split in A+x and B+x; that
is typical of binary matroids. A weaker property would be that each
circuit (of length >=k) ''spans'' an element x not in C: then there must
be a proper subset A of C so that A+x is a circuit, and by circuit
elimination a subset B of C so that B+x is a circuit and A union B = C. In
a binary matroid such A and B are necessarily disjoint, in general
matroids this is not necessary.
Binary matroids are chacterized by the fact that if C, C'are circuits,
then the symmetric difference of C and C' is the disjoint union of
circuits.
--
Ticket URL: <http://trac.sagemath.org/ticket/18484#comment:9>
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.