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  2. Linear inequality - Wikipedia

    en.wikipedia.org/wiki/Linear_inequality

    For example, [3] to draw the solution set of x + 3y < 9, one first draws the line with equation x + 3y = 9 as a dotted line, to indicate that the line is not included in the solution set since the inequality is strict. Then, pick a convenient point not on the line, such as (0,0).

  3. Crossing number inequality - Wikipedia

    en.wikipedia.org/wiki/Crossing_number_inequality

    The crossing number inequality states that, for an undirected simple graph G with n vertices and e edges such that e > 7n, the crossing number cr(G) obeys the inequality ⁡ (). The constant 29 is the best known to date, and is due to Ackerman. [3]

  4. Inequality (mathematics) - Wikipedia

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

    In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. [1] It is used most often to compare two numbers on the number line by their size. The main types of inequality are less than (<) and greater than (>).

  5. Planar graph - Wikipedia

    en.wikipedia.org/wiki/Planar_graph

    In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross each other. [1] [2] Such a drawing is called a plane graph, or a planar embedding of the graph.

  6. Jensen's inequality - Wikipedia

    en.wikipedia.org/wiki/Jensen's_inequality

    Jensen's inequality generalizes the statement that a secant line of a convex function lies above its graph. Visualizing convexity and Jensen's inequality. In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function.

  7. Cheeger constant (graph theory) - Wikipedia

    en.wikipedia.org/wiki/Cheeger_constant_(graph...

    In mathematics, the Cheeger constant (also Cheeger number or isoperimetric number) of a graph is a numerical measure of whether or not a graph has a "bottleneck". The Cheeger constant as a measure of "bottleneckedness" is of great interest in many areas: for example, constructing well-connected networks of computers, card shuffling.

  8. Lorenz curve - Wikipedia

    en.wikipedia.org/wiki/Lorenz_curve

    It was developed by Max O. Lorenz in 1905 for representing inequality of the wealth distribution. The curve is a graph showing the proportion of overall income or wealth assumed by the bottom x% of the people, although this is not rigorously true for a finite

  9. Homomorphism density - Wikipedia

    en.wikipedia.org/wiki/Homomorphism_density

    The effect of applying the Cauchy-Schwarz inequality is "folding" the graph over a line of symmetry to relate it to a smaller graph. This allows for the reduction of densities of large but symmetric graphs to that of smaller graphs. As an example, we prove that the cycle of length 4 is Sidorenko. If the vertices are labelled 1,2,3,4 in that ...

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