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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.
In combinatorial optimization, a field within mathematics, the linear bottleneck assignment problem (LBAP) is similar to the linear assignment problem. [1] In plain words the problem is stated as follows: There are a number of agents and a number of tasks.
Otherwise, it is called unbalanced assignment. [1] If the total cost of the assignment for all tasks is equal to the sum of the costs for each agent (or the sum of the costs for each task, which is the same thing in this case), then the problem is called linear assignment.
The relative strength of two systems of formal logic can be defined via model theory. Specifically, a logic α {\displaystyle \alpha } is said to be as strong as a logic β {\displaystyle \beta } if every elementary class in β {\displaystyle \beta } is an elementary class in α {\displaystyle \alpha } .
[1] [2] This applies even in the cases that f(x) and g(x) take on different values at c, or are discontinuous at c. Polynomials and functions of the form x a
Hilbert proposed a program at the beginning of the 20th century whose ultimate goal was to show, using mathematical methods, the consistency of mathematics. Since most mathematical disciplines can be reduced to arithmetic , the program quickly became the establishment of the consistency of arithmetic by methods formalizable within arithmetic ...
In an undirected simple graph of order n, the maximum degree of each vertex is n − 1 and the maximum size of the graph is n(n − 1) / 2 . The edges of an undirected simple graph permitting loops G {\displaystyle G} induce a symmetric homogeneous relation ∼ {\displaystyle \sim } on the vertices of G {\displaystyle G} that is called ...
[1] In his 1821 book Cours d'analyse, Augustin-Louis Cauchy discussed variable quantities, infinitesimals and limits, and defined continuity of = by saying that an infinitesimal change in x necessarily produces an infinitesimal change in y, while Grabiner claims that he used a rigorous epsilon-delta definition in proofs. [2]