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# 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} }

- Published 1979 in J. Comb. Theory, Ser. B
DOI:10.1016/0095-8956(79)90018-2

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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