Strong Splitter Theorem
نویسندگان
چکیده
منابع مشابه
Towards 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...
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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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In 1960 Berge came up with the concept of perfect graphs, and in doing so, conjectured some characteristics about them. A perfect graph is a graph in which the chromatic number of every induced subgraph equals the size of the largest clique of that subgraph [2]. Two conjectures are now known as the Perfect Graph Theorem and the Strong Perfect Graph Theorem. Both of these theorems make deteminin...
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ژورنال
عنوان ژورنال: Annals of Combinatorics
سال: 2013
ISSN: 0218-0006,0219-3094
DOI: 10.1007/s00026-013-0214-5