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In graph theory, the Nash-Williams theorem is a tree-packing theorem that describes how many edge-disjoint spanning trees (and more generally forests) a graph can have:. A graph G has t edge-disjoint spanning trees iff for every partition , …, where there are at least t(k − 1) crossing edges (Tutte 1961, Nash-Williams 1961).
A cut C = (S, T) is a partition of V of a graph G = (V, E) into two subsets S and T. The cut-set of a cut C = (S, T) is the set {(u, v) ∈ E | u ∈ S, v ∈ T} of edges that have one endpoint in S and the other endpoint in T. If s and t are specified vertices of the graph G, then an s – t cut is a cut in which s belongs to the set S and t ...
A carving decomposition is an unrooted binary tree with each leaf representing a vertex in the original graph, and the width of a cut is the number (or total weight in a weighted graph) of edges that are incident to a vertex in both subtrees. Branch width algorithms typically work by reducing to an equivalent carving width problem.
• Restore your browser's default settings in Edge • Restore your browser's default settings in Safari • Restore your browser's default settings in Firefox • Restore your browser's default settings in Chrome. While Internet Explorer may still work with some AOL products, it's no longer supported by Microsoft and can't be updated.
A graph and two of its cuts. The dotted line in red is a cut with three crossing edges. The dashed line in green is a min-cut of this graph, crossing only two edges. In computer science and graph theory, Karger's algorithm is a randomized algorithm to compute a minimum cut of a connected graph. It was invented by David Karger and first ...
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The next largest edge is edge BD so the algorithm will check this edge and delete the edge. The next edge to check is edge EG, which will not be deleted since it would disconnect node G from the graph. Therefore, the next edge to delete is edge BC. The next largest edge is edge EF so the algorithm will check this edge and delete the edge.
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