The 3-connected matroids with circumference 6
نویسندگان
چکیده
منابع مشابه
The 3-connected matroids with circumference 6
We construct all 3-connected matroids with circumference equal to 6 having rank at least 8. A matroid belongs to this family if and only if it is a generalized parallel connection of a set of planes along a common line (which may have some virtual points).
متن کاملThe 3-connected binary matroids with circumference 6 or 7
In this paper, we construct all 3-connected binary matroids with circumference equal to 6 or 7 having large rank. © 2008 Elsevier Ltd. All rights reserved.
متن کاملThe 3-connected Binary Matroids with Circumference
In this paper, we construct all 3-connected binary matroids with circumference equal to 6 or 7 having large rank.
متن کاملOn size, circumference and circuit removal in 3-connected matroids
This paper proves several extremal results for 3-connected matroids. In particular, it is shown that, for such a matroid M , (i) if the rank r(M) of M is at least six, then the circumference c(M) of M is at least six and, provided |E(M)| ≥ 4r(M)− 5, there is a circuit whose deletion from M leaves a 3-connected matroid; (ii) if r(M) ≥ 4 and M has a basis B such that M\e is not 3-connected for al...
متن کاملOn Nonbinary 3-connected Matroids
It is well known that a matroid is binary if and only if it has no minor isomorphic to U2,4, the 4-point line. Extending this result, Bixby proved that every element in a nonbinary connected matroid is in a U2,4minor. The result was further extended by Seymour who showed that every pair of elements in a nonbinary 3-connected matroid is in a U2,4-minor. This paper extends Seymour's theorem by pr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2010
ISSN: 0012-365X
DOI: 10.1016/j.disc.2010.01.001