The Excluded Minors for the Matroids That Are Binary or Ternary
نویسندگان
چکیده
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.
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 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.
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