Branch-Width and Rota's Conjecture
نویسندگان
چکیده
منابع مشابه
Branch-Width and Rota's Conjecture
We begin by giving some background to this result. A matroid M is an excluded minor for a minor-closed class of matroids if M is not in the class but all proper minors of M are. It is natural to attempt to characterize a minor-closed class of matroids by giving a complete list of its excluded minors. Unfortunately, a minor-closed class of matroids can have an infinite number of excluded minors....
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We construct a polynomial-time algorithm to approximate the branch-width of certain symmetric submodular functions, and give two applications. The first is to graph “clique-width”. Clique-width is a measure of the difficulty of decomposing a graph in a kind of tree-structure, and if a graph has clique-width at most k then the corresponding decomposition of the graph is called a “k-expression”. ...
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An integer-valued function f on the set 2V of all subsets of a finite set V is a connectivity function if it satisfies the following conditions: (1) f(X) + f(Y ) ≥ f(X ∩Y )+ f(X ∪Y ) for all subsets X, Y of V , (2) f(X) = f(V \X) for all X ⊆ V , and (3) f(∅) = 0. Branch-width is defined for graphs, matroids, and more generally, connectivity functions. We show that for each constant k, there is ...
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متن کاملMatroid 3-connectivity and branch width
We prove that, for each nonnegative integer k and each matroid N , if M is a 3-connected matroid containing N as a minor, and the the branch width of M is sufficiently large, then there is a k-element set X ⊆ E(M) such that one of M \X and M/X is 3-connected and contains N as a minor.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2002
ISSN: 0095-8956
DOI: 10.1006/jctb.2002.2130