Search results
Results From The WOW.Com Content Network
An example of an ear decomposition of a graph containing 3 ears. In graph theory, an ear of an undirected graph G is a path P where the two endpoints of the path may coincide, but where otherwise no repetition of edges or vertices is allowed, so every internal vertex of P has degree two in G.
In graph theory, the Gallai–Edmonds decomposition is a partition of the vertices of a graph into three subsets which provides information on the structure of maximum matchings in the graph. Tibor Gallai [1] [2] and Jack Edmonds [3] independently discovered it and proved its key properties. The Gallai–Edmonds decomposition of a graph can be ...
Graph theory is also widely used in sociology as a way, for example, to measure actors' prestige or to explore rumor spreading, notably through the use of social network analysis software. Under the umbrella of social networks are many different types of graphs. [ 17 ]
Branch decomposition of a grid graph, showing an e-separation.The separation, the decomposition, and the graph all have width three. In graph theory, a branch-decomposition of an undirected graph G is a hierarchical clustering of the edges of G, represented by an unrooted binary tree T with the edges of G as its leaves.
According to Robbins' theorem, an undirected graph may be oriented in such a way that it becomes strongly connected, if and only if it is 2-edge-connected. One way to prove this result is to find an ear decomposition of the underlying undirected graph and then orient each ear consistently. [12]
An example graph G with pathwidth 2 and its path-decomposition of width 2. The bottom portion of the image is the same graph and path-decomposition with color added for emphasis. (This example is an adaptation of the graph presented in Bodlaender (1994a), emphasis added)
Walecki's Hamiltonian decomposition of the complete graph . In graph theory, a branch of mathematics, a Hamiltonian decomposition of a given graph is a partition of the edges of the graph into Hamiltonian cycles. Hamiltonian decompositions have been studied both for undirected graphs and for directed graphs.
The decomposition depicted in the figure below is this special decomposition for the given graph. A graph, its quotient where "bags" of vertices of the graph correspond to the children of the root of the modular decomposition tree, and its full modular decomposition tree: series nodes are labeled "s", parallel nodes "//" and prime nodes "p".