#18784: Tutte connectors for matroids
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Reporter: Rudi | Owner: Rudi
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.8
Component: matroid theory | Resolution:
Keywords: | Merged in:
Authors: Rudi Pendavingh | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/Rudi/tutte_connectors_for_matroids|
494f04a7c37a4d0682ec34feaee6127a514b44a1
Dependencies: | Stopgaps:
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Description changed by Rudi:
Old description:
> Tutte's linking theorem states that if `S`, `T` are disjoint subsets of
> the ground set of a matroid `M`, then
> `\min\{\lambda_M(X): S\subseteq X, X\cap T =\emptyset\}`
> equals
> `\max\{\lambda_N(S): E(N)=S\cup T, N= M\setminus I/ J\}`
> Here `\lambda_M(X):=r_M(X)+r_M(E-X)-r_M(E)` is the connectivity of `X` in
> `M`.
>
> Write a function that outputs both an optimal `X` (a min separation)
> and an optimal `I` (a max connector) as in Tutte's linking theorem.
New description:
Tutte's linking theorem states that if `S`, `T` are disjoint subsets of
the ground set of a matroid `M`, then
`\min\{\lambda_M(X): S\subseteq X, X\cap T =\emptyset\}`
equals
`\max\{\lambda_N(S): E(N)=S\cup T, N= M/I\setminus J\}`
Here `\lambda_M(X):=r_M(X)+r_M(E-X)-r_M(E)` is the connectivity of `X` in
`M`.
Write a function that outputs both an optimal `X` (a min separation) and
an optimal `I` (a max connector) as in Tutte's linking theorem.
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Ticket URL: <http://trac.sagemath.org/ticket/18784#comment:8>
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