The Regular Excluded Minors for Signed-Graphic Matroids
نویسندگان
چکیده
منابع مشابه
The 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.
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In unpublished work, Geelen proved that a matroid is nearregular if and only if it has no minor isomorphic to U2,5, U3,5, F7, F ∗ 7 , F− 7 , (F − 7 ) ∗, AG(2, 3)\e, (AG(2,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: Combinatorics, Probability and Computing
سال: 2009
ISSN: 0963-5483,1469-2163
DOI: 10.1017/s0963548309990241