Capturing matroid elements in unavoidable 3-connected minors

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Capturing matroid elements in unavoidable 3-connected minors

A result of Ding, Oporowski, Oxley, and Vertigan reveals that a large 3-connectedmatroidM has unavoidable structure. For everyn > 2, there is an integer f (n) so that if |E(M)| > f (n), thenM has aminor isomorphic to the rank-n wheel or whirl, a rank-n spike, the cycle or bond matroid of K3,n, or U2,n or Un−2,n. In this paper, we build on this result to determine what can be said about a large ...

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ژورنال

عنوان ژورنال: European Journal of Combinatorics

سال: 2012

ISSN: 0195-6698

DOI: 10.1016/j.ejc.2012.01.012