Infinite subgraphs as matroid circuits

@article{Matthews1979InfiniteSA,
  title={Infinite subgraphs as matroid circuits},
  author={Laurence R. Matthews},
  journal={J. Comb. Theory, Ser. B},
  year={1979},
  volume={27},
  pages={260-273}
}
A matroidal family V is defined to be a collection of graphs such that, for any given graph G, the subgraphs of G isomorphic to a graph in V satisfy the matroid circuit-axioms. Here matroidal families closed under homeomorphism are considered. A theorem of Simks-Pereira shows that when only finite connected graphs are allowed as members of Q, two matroids arise: the cycle matroid and bicircular matroid. Here this theorem is generalized in two directions: the graphs are allowed to be infinite… CONTINUE READING

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