Partitioning Matroids With Only Small Cocircuits
نویسنده
چکیده
منابع مشابه
Regular Matroids with Graphic Cocircuits
In this paper we examine the effect of removing cocircuits from regular matroids and we focus on the case in which such a removal always results in a graphic matroid. The first main result, given in section 3, is that a regular matroid with graphic cocircuits is signed-graphic if and only if it does not contain two specific minors. This provides a useful connection between graphic, regular and ...
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The number of disjoint cocircuits in a matroid is bounded by its rank. There are, however, matroids with arbitrarily large rank that do not contain two disjoint cocircuits; consider, for example, M(Kn) and Un,2n. Also the bicircular matroids B(Kn) have arbitrarily large rank and have no 3 disjoint cocircuits. We prove that for each k and n there exists a constant c such that, if M is a matroid ...
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Bixby and Cunningham showed that a 3-connected binary matroid M is graphic if and only if every element belongs to at most two non-separating cocircuits. Likewise, Lemos showed that such a matroid M is graphic if and only if it has exactly r(M) + 1 nonseparating cocircuits. Hence the presence inM of either an element in at least three non-separating cocircuits, or of at least r(M) + 2 non-separ...
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We prove that, for any positive integers k, n, and q, if M is a simple matroid that has neither a U2,q+2nor an M(Kn)minor and M has sufficiently large rank, then M has a cocircuit of size at most r(M)/k.
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We prove that, for any positive integers n; k and q; there exists an integer R such that, if M is a matroid with no MðKnÞor U2;qþ2-minor, then either M has a collection of k disjoint cocircuits or M has rank at most R: Applied to the class of cographic matroids, this result implies the edge-disjoint version of the Erdös–Pósa Theorem. r 2002 Elsevier Science (USA). All rights reserved. AMS 1991 ...
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عنوان ژورنال:
- Combinatorics, Probability & Computing
دوره 11 شماره
صفحات -
تاریخ انتشار 2002