منابع مشابه
Testing branch-width
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 ...
متن کاملApproximating clique-width and branch-width
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”. ...
متن کاملBranch-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....
متن کاملRank-width is less than or equal to branch-width
We prove that the rank-width of the incidence graph of a graph G is either equal to or exactly one less than the branch-width of G, unless the maximum degree of G is 0 or 1. This implies that rank-width of a graph is less than or equal to branch-width of the graph unless the branch-width is 0. Moreover, this inequality is tight.
متن کاملBranch-and-Prune trees with bounded width
The Molecular Distance Geometry Problem, which asks to find the embedding in R of a given weighted undirected graph, is a good model for determining the structure of proteins given a set of inter-atomic distances [6,4]. Its generalization to R is called Distance Geometry Problem (DGP), which has applications in wireless sensor networks [2] and graph drawing. In general, the MDGP and DGP implici...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2007
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2006.06.006