Matroids of Gain Graphs in Applied Discrete Geometry

@inproceedings{Tanigawa2012MatroidsOG,
  title={Matroids of Gain Graphs in Applied Discrete Geometry},
  author={Shin-ichi Tanigawa},
  year={2012}
}
A G-gain graph is a graph whose oriented edges are labeled invertibly from a group G. Zaslavsky proposed two matroids of G-gain graphs, called frame matroids and lift matroids, and investigated linear representations of them. Each matroid has a canonical representation over a field F if G is isomorphic to a subgroup of F^{\times} in the case of frame matroids or G is isomorphic to an additive subgroup of F in the case of lift matroids. The canonical representation of the frame matroid of a… CONTINUE READING

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