The excluded minors for the class of matroids that are binary or ternary
نویسندگان
چکیده
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.
منابع مشابه
On 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 Excluded Minors for the Matroids That Are Binary or Ternary
We show that a matroid is binary or ternary if and only if it has no minor isomorphic to U2,5, U3,5, U2,4 ⊕ F7, U2,4 ⊕ F ∗ 7 , U2,4 ⊕2 F7, U2,4 ⊕2 F ∗ 7 , or the unique matroids obtained by relaxing a circuit-hyperplane 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 کاملThe Excluded Minors for GF(4)-Representable Matroids
The definitions of these matroids, with a summary of their interesting properties, can be found in the Appendix. Except for P"8 , they were all known to be excluded minors for GF(4)-representability (see Oxley [15, 17]). The matroid P"8 is obtained by relaxing the unique pair of disjoint circuit-hyperplanes of P8 . Ever since Whitney's introductory paper [28] on matroid theory, researchers have...
متن کاملOn Representable Matroids Having Neither U2,5– Nor U3,5–minors
Consider 3–connected matroids that are neither binary nor ternary and have neither U2,5– nor U3,5–minors: for example, AG(3, 2)′, the matroid obtained by relaxing a circuit-hyperplane of AG(3, 2). The main result of the paper shows that no matroid of this sort is representable over any field. This result makes it possible to extend known characterisations of the binary and ternary matroids repr...
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