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Consider a graph G = (V, E), where V denotes the set of n vertices and E the set of edges. For a (k,v) balanced partition problem, the objective is to partition G into k components of at most size v · (n/k), while minimizing the capacity of the edges between separate components. [1]
The input to the algorithm is an undirected graph G = (V, E) with vertex set V, edge set E, and (optionally) numerical weights on the edges in E.The goal of the algorithm is to partition V into two disjoint subsets A and B of equal (or nearly equal) size, in a way that minimizes the sum T of the weights of the subset of edges that cross from A to B.
In graph theory, the Graham–Pollak theorem states that the edges of an -vertex complete graph cannot be partitioned into fewer than complete bipartite graphs. [1] It was first published by Ronald Graham and Henry O. Pollak in two papers in 1971 and 1972 (crediting Hans Witsenhausen for a key lemma), in connection with an application to ...
In graph theory, the strength of an undirected graph corresponds to the minimum ratio of edges removed/components created in a decomposition of the graph in question. It is a method to compute partitions of the set of vertices and detect zones of high concentration of edges, and is analogous to graph toughness which is defined similarly for vertex removal.
The dotted line in red represents a cut with three crossing edges. The dashed line in green represents one of the minimum cuts of this graph, crossing only two edges. [1] In graph theory, a minimum cut or min-cut of a graph is a cut (a partition of the vertices of a graph into two disjoint subsets) that is minimal in some metric.
Scale-free network; Snark (graph theory) Sparse graph. Sparse graph code; Split graph; ... Graph partition; Graph pebbling; Graph property; Graph reduction; Graph ...
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