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  2. List of NP-complete problems - Wikipedia

    en.wikipedia.org/wiki/List_of_NP-complete_problems

    Steiner tree, or Minimum spanning tree for a subset of the vertices of a graph. [2] (The minimum spanning tree for an entire graph is solvable in polynomial time.) Modularity maximization [5] Monochromatic triangle [3]: GT6 Pathwidth, [6] or, equivalently, interval thickness, and vertex separation number [7] Rank coloring; k-Chinese postman

  3. Erdős–Gallai theorem - Wikipedia

    en.wikipedia.org/wiki/Erdős–Gallai_theorem

    The Erdős–Gallai theorem is a result in graph theory, a branch of combinatorial mathematics.It provides one of two known approaches to solving the graph realization problem, i.e. it gives a necessary and sufficient condition for a finite sequence of natural numbers to be the degree sequence of a simple graph.

  4. Young's inequality for products - Wikipedia

    en.wikipedia.org/wiki/Young's_inequality_for...

    Proof [2]. Since + =, =. A graph = on the -plane is thus also a graph =. From sketching a visual representation of the integrals of the area between this curve and the axes, and the area in the rectangle bounded by the lines =, =, =, =, and the fact that is always increasing for increasing and vice versa, we can see that upper bounds the area of the rectangle below the curve (with equality ...

  5. Bernoulli's inequality - Wikipedia

    en.wikipedia.org/wiki/Bernoulli's_inequality

    Bernoulli's inequality can be proved for case 2, in which is a non-negative integer and , using mathematical induction in the following form: we prove the inequality for {,}, from validity for some r we deduce validity for +.

  6. List of inequalities - Wikipedia

    en.wikipedia.org/wiki/List_of_inequalities

    Bennett's inequality, an upper bound on the probability that the sum of independent random variables deviates from its expected value by more than any specified amount Bhatia–Davis inequality , an upper bound on the variance of any bounded probability distribution

  7. Constraint (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Constraint_(mathematics)

    If an inequality constraint holds as a strict inequality at the optimal point (that is, does not hold with equality), the constraint is said to be non-binding, as the point could be varied in the direction of the constraint, although it would not be optimal to do so. Under certain conditions, as for example in convex optimization, if a ...