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On packing minors into connected matroids
Authors
Manoel Lemos
James Oxley
Publication date
28 July 1998
Publisher
LSU Digital Commons
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Abstract
Let N be a matroid with k connected components and M be a minor-minimal connected matroid having N as a minor. This note proves that |E(M) - E(N)| is at most 2k - 2 unless N or its dual is free, in which case |E(M) - E(N)| ≤k - 1. Examples are given to show that these bounds are best possible for all choices for N. A consequence of the main result is that a minimally connected matroid of rank r and maximum circuit size c has at most 2r - c + 2 elements. This bound sharpens a result of Murty. © 1998 Elsevier Science B.V. All rights reserved
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Last time updated on 06/05/2017
Louisiana State University
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