#18784: Tutte connectors for matroids
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Reporter: Rudi | Owner: Rudi
Type: enhancement | Status: positive_review
Priority: major | Milestone: sage-6.8
Component: matroid theory | Resolution:
Keywords: | Merged in:
Authors: Rudi Pendavingh | Reviewers: Chao Xu
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/Rudi/tutte_connectors_for_matroids|
9d932ee9b5e693b46fd7bfbd0da2ebb1d1bfdcc2
Dependencies: | Stopgaps:
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Changes (by chaoxu):
* status: needs_review => positive_review
* reviewer: => Chao Xu
Comment:
Hi Rudi,
Positive review.
Here are more things I have tried:
Some 4-connected(and not 5-connected) binary matroids given by Gordon
Royle.
each list is a matroid and each number in the list expressed in binary is
a column of a matrix representing the matroid.
{{{
[[1,2,4,7,8,11,13,14,16,21,25,31],
[1,2,4,8,15,16,21,25,32,41,51,63],
[1,2,4,8,15,16,21,22,32,41,42,51],
[1,2,4,7,8,13,16,31,32,35,52,61],
[1,2,4,8,15,16,32,54,64,90,109,113],
[1,2,4,7,8,11,13,14,16,19,21,22,25,31],
[1,2,4,8,15,16,21,25,30,32,37,41,44,51],
[1,2,4,8,15,16,21,25,30,32,37,41,46,51],
[1,2,4,8,15,16,21,25,30,32,37,41,51,52],
[1,2,4,8,15,16,21,25,30,32,37,41,51,54],
[1,2,4,8,15,16,21,27,28,32,39,41,51,56],
[1,2,4,8,15,16,21,22,27,28,32,41,42,51],
[1,2,4,8,15,16,21,22,27,32,39,41,42,51],
[1,2,4,8,15,16,21,22,27,32,41,42,44,51],
[1,2,4,8,15,16,21,22,32,41,42,51,61,62],
[1,2,4,7,8,11,13,14,16,19,21,22,25,26,28,31],
[1,2,4,8,15,16,21,25,30,32,37,41,46,51,52,56],
[1,2,4,8,15,16,21,25,30,32,37,41,46,51,54,56],
[1,2,4,8,15,16,21,25,30,32,37,41,46,51,54,58],
[1,2,4,8,15,16,21,27,28,32,39,41,44,51,52,56],
[1,2,4,8,15,16,21,22,27,28,32,39,41,42,51,52],
[1,2,4,8,15,16,21,22,27,28,32,39,41,42,44,51],
[1,2,4,8,15,16,21,22,27,32,39,41,42,51,61,62],
[1,2,4,7,8,11,13,14,16,19,22,31,32,35,52,61],
[1,2,4,7,8,11,13,14,16,19,28,31,32,35,52,61]]
}}}
Applying `is_kconnected(4)` and `is_kconnecte(5)` returns desired results.
--
Ticket URL: <http://trac.sagemath.org/ticket/18784#comment:25>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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