# co spanning tree

Hi,

Does anyone know that what is co spanning tree. If there are some good answers then it would be really good to have an example also.

Thanks

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Can you explain in what context this term came up? – Sebastian Oct 4 '11 at 14:11
I would guess that it has to do with matroid duality, where the convention is to prefix everything in the dual with a co. So a cobasis is a basis in the dual, a cocircuit is a circuit in the dual, etc. If you regard a spanning tree as a basis for the graphic matroid, then a cospanning tree is just a basis in the dual, namely the complement of a spanning tree. I think it is time that someone invented the matroid term conut, so that a conut in the dual would be a... – Tony Huynh Oct 4 '11 at 14:24

The paper here uses this name for the complement of a spanning tree, i.e. the set of edges which do not lie in some given spanning tree.

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That is also what I would expect it to mean. It is pretty much the same as Tony Huynh's comment: the complement of a spanning tree is a base for the dual matroid. If the given graph is planar, it is (the set of edges that dualize to) a spanning tree of the dual graph. – David Eppstein Oct 7 '11 at 16:10

If $G = (V, E)$ has a spanning tree $T = (V, E_1)$, the cospanning tree of $T$ is a spanning subgraph of $G$, defined by $(V, E-E_1)$.

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