Search results
Results from the WOW.Com Content Network
The induced width of an ordered graph is the width of its induced graph. [2] Given an ordered graph, its induced graph is another ordered graph obtained by joining some pairs of nodes that are both parents of another node. In particular, nodes are considered in turn according to the ordering, from last to first. For each node, if two of its ...
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 formed from a given graph by deleting one vertex, especially in the context of the reconstruction conjecture. See also deck, the multiset of all cards of a graph. carving width Carving width is a notion of graph width analogous to branchwidth, but using hierarchical clusterings of vertices instead of hierarchical clusterings of edges.
Decomposition, defined as partitioning the edge set of a graph (with as many vertices as necessary accompanying the edges of each part of the partition), has a wide variety of questions. Often, the problem is to decompose a graph into subgraphs isomorphic to a fixed graph; for instance, decomposing a complete graph into Hamiltonian cycles.
In geometry and kinematics, coordinate systems are used to describe the (linear) position of points and the angular position of axes, planes, and rigid bodies. [16] In the latter case, the orientation of a second (typically referred to as "local") coordinate system, fixed to the node, is defined based on the first (typically referred to as ...
The graphs can be used together to determine the economic equilibrium (essentially, to solve an equation). Simple graph used for reading values: the bell-shaped normal or Gaussian probability distribution, from which, for example, the probability of a man's height being in a specified range can be derived, given data for the adult male population.
There exist fixed-parameter tractable algorithms to solve the metric dimension problem for the parameters "vertex cover", [13] "max leaf number", [14] and "modular width". [9] Graphs with bounded cyclomatic number, vertex cover number or max leaf number all have bounded treewidth, however it is an open problem to determine the complexity of the ...
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.