Properties of matroids characterizable in terms of excluded matroids
نویسندگان
چکیده
منابع مشابه
The Excluded Minors for Gf(4)--representable Matroids the Excluded Minors for Gf(4){representable Matroids
There are exactly seven excluded minors for the class of GF(4){representable matroids. Note: The research for this paper was carried out under the PNA1.1-project P&BS of CWI, while J.F. Geelen and A. Kapoor visited the CWI in Amsterdam with nancial support from EIDMA.
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In unpublished work, Geelen proved that a matroid is nearregular if and only if it has no minor isomorphic to U2,5, U3,5, F7, F ∗ 7 , F− 7 , (F − 7 ) ∗, AG(2, 3)\e, (AG(2,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.
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This paper strengthens the excluded-minor characterization of GF(4)-representable matroids. In particular, it is shown that there are only finitely many 3-connected matroids that are not GF(4)-representable and that have no U2, 6 -, U4, 6 -, P6 -, F & 7 -, or (F & 7 )*-minors. Explicitly, these matroids are all minors of S(5, 6, 12) with rank and corank at least 4, and P"8 , the matroid that ca...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1983
ISSN: 0095-8956
DOI: 10.1016/0095-8956(83)90023-0