Let M be a representable matroid and Q,R, S, T subsets of the ground set such that the smallest separation that separates Q from R has order k, and the smallest separation that separates S from T has order l. We prove that if M is sufficiently large, then there is an element e such that in one of M\e and M/e both connectivities are preserved. For matroids representable over a finite field we prove a stronger result: we show that we can remove e such that both a connectivity and a minor of M are preserved. © 2014 Society for Industrial and Applied Mathematics.
Intertwining connectivities in representable matroids / Huynh, T.; Van Zwam, S. H. M.. - In: SIAM JOURNAL ON DISCRETE MATHEMATICS. - ISSN 0895-4801. - 28:1(2014), pp. 188-196. [10.1137/13091837X]
Intertwining connectivities in representable matroids
Huynh T.;
2014
Abstract
Let M be a representable matroid and Q,R, S, T subsets of the ground set such that the smallest separation that separates Q from R has order k, and the smallest separation that separates S from T has order l. We prove that if M is sufficiently large, then there is an element e such that in one of M\e and M/e both connectivities are preserved. For matroids representable over a finite field we prove a stronger result: we show that we can remove e such that both a connectivity and a minor of M are preserved. © 2014 Society for Industrial and Applied Mathematics.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
