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- W4300145611 abstract "Adding elements to matroids can be fraught with difficulty. In the V'amos matroid $V_8$, there are four independent sets $X_1,X_2, X_3,$ and $X_4$ such that $(X_1 cup X_2,X_3 cup X_4)$ is a $3$-separation while exactly three of the local connectivities $sqcap(X_1,X_{3})$, $sqcap(X_1,X_{4})$, $sqcap(X_2,X_{3})$, and $sqcap(X_2,X_{4})$ are one, with the fourth being zero. As is well known, there is no extension of $V_8$ by a non-loop element $p$ such that $X_j cup p$ is a circuit for all $j$. This paper proves that a matroid can be extended by a fixed element in the guts of a $3$-separation provided no V'amos-like structure is present." @default.
- W4300145611 created "2022-10-03" @default.
- W4300145611 creator A5050893955 @default.
- W4300145611 date "2018-05-13" @default.
- W4300145611 modified "2023-09-25" @default.
- W4300145611 title "A matroid extension result" @default.
- W4300145611 doi "https://doi.org/10.48550/arxiv.1805.04960" @default.
- W4300145611 hasPublicationYear "2018" @default.
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