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On matroids on edge sets of graphs with connected subgraphs as circuits


Author: J. M. S. Sim oes-Pereira
Journal: Proc. Amer. Math. Soc. 38 (1973), 503-506
MSC: Primary 05B35
DOI: https://doi.org/10.1090/S0002-9939-1973-0314663-6
MathSciNet review: 0314663
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Abstract: It is proved that if $ \mathcal{F}$ is a finite family of connected, finite graphs, then a graph $ G$ exists such that the subgraphs of $ G$ isomorphic to a member of the family cannot be regarded as the circuits of a matroid on the edge set of $ G$.


References [Enhancements On Off] (What's this?)

  • [1] J. M. S. Simões-Pereira, Subgraphs as matroid cells, Math. Z. 127 (1972), 315-322. MR 0317973 (47:6522)
  • [2] H. Whitney, On the abstract properties of linear dependence, Amer. J. Math. 57 (1935), 501-533. MR 1507091

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0314663-6
Keywords: Matroid, graph, matroid circuit, subgraph, subgraphs as matroid circuits
Article copyright: © Copyright 1973 American Mathematical Society

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