Search results
Results from the WOW.Com Content Network
The commutative diagram used in the proof of the five lemma. In mathematics, and especially in category theory, a commutative diagram is a diagram such that all directed paths in the diagram with the same start and endpoints lead to the same result. [1] It is said that commutative diagrams play the role in category theory that equations play in ...
A three-dimensional hypercube graph showing a Hamiltonian path in red, and a longest induced path in bold black. In graph theory, a path in a graph is a finite or infinite sequence of edges which joins a sequence of vertices which, by most definitions, are all distinct (and since the vertices are distinct, so are the edges).
A path is a particularly simple example of a tree, and in fact the paths are exactly the trees in which no vertex has degree 3 or more. A disjoint union of paths is called a linear forest . Paths are fundamental concepts of graph theory, described in the introductory sections of most graph theory texts.
Parity graphs include the distance-hereditary graphs, in which every two induced paths between the same two vertices have the same length.They also include the bipartite graphs, which may be characterized analogously as the graphs in which every two paths (not necessarily induced paths) between the same two vertices have the same parity, and the line perfect graphs, a generalization of the ...
In the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once. A Hamiltonian cycle (or Hamiltonian circuit) is a cycle that visits each vertex exactly once. A Hamiltonian path that starts and ends at adjacent vertices can be completed by adding ...
The causal future of relative to , + [;], is the causal future of considered as a submanifold of . Note that this is quite a different concept from J + [ S ] ∩ T {\displaystyle J^{+}[S]\cap T} which gives the set of points in T {\displaystyle T} which can be reached by future-directed causal curves starting from S {\displaystyle S} .
In mathematics, especially in the areas of abstract algebra dealing with group cohomology or relative homological algebra, Shapiro's lemma, also known as the Eckmann–Shapiro lemma, relates extensions of modules over one ring to extensions over another, especially the group ring of a group and of a subgroup. It thus relates the group ...
In statistics, econometrics, epidemiology, genetics and related disciplines, causal graphs (also known as path diagrams, causal Bayesian networks or DAGs) are probabilistic graphical models used to encode assumptions about the data-generating process. Causal graphs can be used for communication and for inference.