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Summary: when do two planted graphs have
the same cotransversal matroid?
federico ardila
amanda ruiz
abstract
Cotransversal matroids are a family of matroids which arise from planted
graphs. We describe when two planted graphs give rise to the same co-
transversal matroid. We define a family of local moves on a planted graph
which preserve the matroid. We prove that if two planted graphs give the
same cotransversal matroid, then they can be obtained from each other by
a series of these local moves.
1 introduction
Cotransversal matroids are a family of matroids which arise from planted graphs.
The goal of this paper is to describe when two planted graphs give rise to the
same cotransversal matroid.
In Sections 2 and 3 we define the operations of swapping and maximizing on a
planted graph (G, B), and prove that these operations preserve the cotransversal
matroid L(G, B). Conversely, in Section 5 we show that any two maximal planted
graph presentations of the same cotransversal matroid can be obtained from each
other by a series of swaps.
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