منابع مشابه
Internally Perfect Matroids
In 1977 Stanley proved that the h-vector of a matroid is an O-sequence and conjectured that it is a pure O-sequence. In the subsequent years the validity of this conjecture has been shown for a variety of classes of matroids, though the general case is still open. In this paper we use Las Vergnas’ internal order to introduce a new class of matroids which we call internally perfect. We prove tha...
متن کاملConstructing Internally 4-connected Binary Matroids
In an earlier paper, we proved that an internally 4connected binary matroid with at least seven elements contains an internally 4-connected proper minor that is at most six elements smaller. We refine this result, by giving detailed descriptions of the operations required to produce the internally 4-connected minor. Each of these operations is top-down, in that it produces a smaller minor from ...
متن کاملTowards a splitter theorem for internally 4-connected binary matroids
In our quest to find a splitter theorem for internally 4-connected binary matroids, we proved in the preceding paper in this series that, except when M or its dual is a cubic Möbius or planar ladder or a certain coextension thereof, an internally 4-connected binary matroid M with an internally 4connected proper minor N either has a proper internally 4-connected minor M ′ with an N -minor such t...
متن کاملInternally 4-connected binary matroids with cyclically sequential orderings
We characterize all internally 4-connected binary matroids M with the property that the ground set of M can be ordered (e0, . . . , en−1) in such a way that {ei, . . . , ei+t} is 4-separating for all 0 ≤ i, t ≤ n − 1 (all subscripts are read modulo n). We prove that in this case either n ≤ 7 or, up to duality, M is isomorphic to the polygon matroid of a cubic or quartic planar ladder, the polyg...
متن کاملTowards a Splitter Theorem for Internally 4-connected Binary Matroids Viii: Small Matroids
Our splitter theorem studies pairs of the form (M,N), where M and N are internally 4-connected binary matroids, M has a proper N -minor, and if M ′ is an internally 4-connected matroid such that M has a proper M ′-minor and M ′ has an N -minor, then |E(M)|− |E(M ′)| > 3. The analysis in the splitter theorem requires the constraint |E(M)| ≥ 16. In this article, we complement that analysis by des...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2017
ISSN: 1077-8926
DOI: 10.37236/5746