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Two-dimensional linear inequalities are expressions in two variables of the form: + < +, where the inequalities may either be strict or not. The solution set of such an inequality can be graphically represented by a half-plane (all the points on one "side" of a fixed line) in the Euclidean plane. [2]
The graph of this function is a line with slope and y-intercept. The functions whose graph is a line are generally called linear functions in the context of calculus . However, in linear algebra , a linear function is a function that maps a sum to the sum of the images of the summands.
Thus we can find a graph with at least e − cr(G) edges and n vertices with no crossings, and is thus a planar graph. But from Euler's formula we must then have e − cr(G) ≤ 3n, and the claim follows. (In fact we have e − cr(G) ≤ 3n − 6 for n ≥ 3). To obtain the actual crossing number inequality, we now use a probabilistic argument.
A graph is said to be rainbow colored if there is a rainbow path between any two pairs of vertices. An edge-colouring of a graph G with colours 1. . . t is an interval t coloring if all colours are used, and the colours of edges incident to each vertex of G are distinct and form an interval of integers.
In graph theory, graph coloring is a methodic assignment of labels traditionally called "colors" to elements of a graph. The assignment is subject to certain constraints, such as that no two adjacent elements have the same color.
The feasible regions of linear programming are defined by a set of inequalities. 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.
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.
The Moore bound is an inequality relating the degree, diameter, and order of a graph, proved by Edward F. Moore. Every Moore graph is a cage. multigraph A multigraph is a graph that allows multiple adjacencies (and, often, self-loops); a graph that is not required to be simple. multiple adjacency