On the Relative Importance of Excluded Minors
نویسندگان
چکیده
If E is a set of matroids, then Ex(E ) denotes the set of matroids that have no minor isomorphic to a member of E . If E ′ ⊆ E , we say that E ′ is superfluous if Ex(E − E ′)− Ex(E ) contains only finitely many 3-connected matroids. We determine the superfluous subsets of six well-known collections of excluded minors. Dedicated, with affection, to “Mathematician, gone 60, left fox with leg trouble. (5, 7)”
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 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 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.
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 کاملA characterization of some graph classes using excluded minors
In this article we present a structural characterization of graphs without K5 and the octahedron as a minor. We introduce semiplanar graphs as arbitrary sums of planar graphs, and give their characterization in terms of excluded minors. Some other excluded minor theorems for 3-connected minors are shown.
متن کامل