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The width of a tree decomposition is the size of its largest set X i minus one. The treewidth tw(G) of a graph G is the minimum width among all possible tree decompositions of G. In this definition, the size of the largest set is diminished by one in order to make the treewidth of a tree equal to one.
The width of a node is the number of its parents, and the width of an ordered graph is the maximal width of its nodes. The induced graph of an ordered graph is obtained by adding some edges to an ordering graph, using the method outlined below. The induced width of an ordered graph is the width of its induced graph. [2] Given an ordered graph ...
While high-end graphing calculators can graph in 3-D, GraphCalc benefits from modern computers' memory, speed, and graphics acceleration ; GraphCalc was developed by Brendan Fields and Mike Arrison, computer science students at Bucknell University, before graduating in 2000. Mike continued the development briefly from 2001–2003, but has since ...
The twin-width of an undirected graph is a natural number associated with the graph, used to study the parameterized complexity of graph algorithms.Intuitively, it measures how similar the graph is to a cograph, a type of graph that can be reduced to a single vertex by repeatedly merging together twins, vertices that have the same neighbors.
It is NP-complete to determine whether a given graph G has treewidth at most a given variable k. [5] However, when k is any fixed constant, the graphs with treewidth k can be recognized, and a width k tree decomposition constructed for them, in linear time. [4] The time dependence of this algorithm on k is an exponential function of k 3.
In this graph, the widest path from Maldon to Feering has bandwidth 29, and passes through Clacton, Tiptree, Harwich, and Blaxhall. In graph algorithms, the widest path problem is the problem of finding a path between two designated vertices in a weighted graph, maximizing the weight of the minimum-weight edge in the path.
The graphs G i may be taken as the induced subgraphs of the sets X i in the first definition of path decompositions, with two vertices in successive induced subgraphs being glued together when they are induced by the same vertex in G, and in the other direction one may recover the sets X i as the vertex sets of the graphs G i. The width of the ...
A graph of cutwidth 2. For the left-to-right vertex ordering shown, each vertical line crosses at most two edges. In graph theory, the cutwidth of an undirected graph is the smallest integer with the following property: there is an ordering of the vertices of the graph, such that every cut obtained by partitioning the vertices into earlier and later subsets of the ordering is crossed by at ...