#18484: Implement k-chordality of a matroid
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       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:
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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.

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Ticket URL: <http://trac.sagemath.org/ticket/18484#comment:9>
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