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

Sim oes-Pereira, J. M. S.

doi:10.1090/S0002-9939-1973-0314663-6

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

On matroids on edge sets of graphs with connected subgraphs as circuits
HTML articles powered by AMS MathViewer

by J. M. S. Sim oes-Pereira PDF

Proc. Amer. Math. Soc. 38 (1973), 503-506 Request permission

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

J. M. S. Simoes-Pereira, On subgraphs as matroid cells, Math. Z. 127 (1972), 315–322. MR 317973, DOI 10.1007/BF01111390
Hassler Whitney, On the Abstract Properties of Linear Dependence, Amer. J. Math. 57 (1935), no. 3, 509–533. MR 1507091, DOI 10.2307/2371182