On internally 4-connected non-regular binary matroids
نویسندگان
چکیده
منابع مشابه
Constructing 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 ...
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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...
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Let M be a matroid. When M is 3-connected, Tutte’s WheelsandWhirls Theorem proves that M has a 3-connected proper minor N with exactly one element fewer than M unless M is a wheel or a whirl. I will present a corresponding result for internally 4-connected binary matroids. This presentation is based on joint work by myself, Dillon Mayhew, and James Oxley.
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We prove that if N is an internally 4-connected minor of an internally 4-connected binary matroid M with E(N) ≥ 4, then there exist matroids M0,M1, . . . ,Mn such that M0 ∼= N , Mn = M , and, for each i ∈ {1, . . . , i}, Mi−1 is a minor of Mi, |E(Mi−1)| ≥ |E(Mi)| − 2, and Mi is 4-connected up to separators of size 5.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2004
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2004.03.001