Publication details
Bridging Separations in Matroids
| Authors | |
|---|---|
| Year of publication | 2005 |
| Type | Article in Periodical |
| Magazine / Source | SIAM Journal on Discrete Mathematics |
| MU Faculty or unit | |
| Citation | |
| Field | General mathematics |
| Keywords | matroid; separation |
| Description | Let $(X_1,X_2)$ be an exact $k$--separation of a matroid $N$. If $M$ is a matroid that contains $N$ as a minor and the $k$--separation $(X_1,X_2)$ does not extend to a $k$--separation in $M$ then we say that $M$ {\em bridges} the $k$--separation $(X_1,X_2)$ in $N$. One would hope that a minor minimal bridge for $(X_1,X_2)$ would not be much larger than $N$. Unfortunately there are instances in which one can construct arbitaraily large minor minimal bridges. We restrict our attention to the class of matroids representable over a fixed finite field and show that here minor minimal bridges are bounded in size. |