The excluded minors for near-regular matroids
نویسندگان
چکیده
In unpublished work, Geelen proved that a matroid is nearregular if and only if it has no minor isomorphic to U2,5, U3,5, F7, F ∗ 7 , F− 7 , (F − 7 ) ∗, AG(2, 3)\e, (AG(2, 3)\e)∗, ∆T (AG(2, 3)\e), or P8. We provide a proof of this characterization.
منابع مشابه
k-Regular Matroids
The class of matroids representable over all fields is the class of regular matroids. The class of matroids representable over all fields except perhaps GF (2) is the class of near-regular matroids. Let k be a non-negative integer. This thesis considers the class of k–regular matroids, a generalization of the last two classes. Indeed, the classes of regular and near-regular matroids coincide wi...
متن کاملOn the Excluded Minors for the Matroids That Are Either Binary or Ternary
The classes of binary and ternary matroids are both relatively well understood as is their intersection, the class of regular matroids. This paper considers the union M of the classes of binary and ternary matroids. M is a minor-closed class and the focus of the paper is on determining its set of excluded minors. It is conjectured here that this set of excluded minors unique matroids that are o...
متن کاملThe Regular Excluded Minors for Signed-Graphic Matroids
We show that the complete list of regular excluded minors for the class of signed-graphic matroids is M(G1), . . . ,M(G29), R15, R16. Here G1, . . . , G29 are the vertically 2-connected excluded minors for the class of projective-planar graphs.
متن کاملThe excluded minors for the class of matroids that are binary or ternary
We show that the excluded minors for the class of matroids that are binary or ternary are U2,5, U3,5, U2,4⊕F7, U2,4⊕F ∗ 7 , U2,4⊕2F7, U2,4 ⊕2 F ∗ 7 , and the unique matroids obtained by relaxing a circuithyperplane in either AG(3, 2) or T12. The proof makes essential use of results obtained by Truemper on the structure of almost-regular matroids.
متن کاملGENERALIZED ∆ − Y EXCHANGE AND k – REGULAR MATROIDS
This paper introduces a generalization of the matroid operation of ∆ − Y exchange. This new operation, segment-cosegment exchange, replaces a coindependent set of k collinear points in a matroid by an independent set of k points that are collinear in the dual of the resulting matroid. The main theorem of the first half of the paper is that, for every field, or indeed partial field, F, the class...
متن کاملAn excluded minors method for infinite matroids
The notion of thin sums matroids was invented to extend the notion of representability to non-finitary matroids. A matroid is tame if every circuit-cocircuit intersection is finite. We prove that a tame matroid is a thin sums matroid over a finite field k if and only if all its finite minors are representable over k. We expect that the method we use to prove this will make it possible to lift m...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Eur. J. Comb.
دوره 32 شماره
صفحات -
تاریخ انتشار 2011