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In a graph, a maximum cut is a cut whose size is at least the size of any other cut. That is, it is a partition of the graph's vertices into two complementary sets S and T, such that the number of edges between S and T is as large as possible. Finding such a cut is known as the max-cut problem. The problem can be stated simply as follows.
Advanced Placement (AP) Microeconomics (also known as AP Micro) is a course offered by the College Board as part of the Advanced Placement Program for high school students interested in college-level coursework in microeconomics and/or gaining advanced standing in college.
The utility maximization problem attempts to explain the action axiom by imposing rationality axioms on consumer preferences and then mathematically modeling and analyzing the consequences. [9] The utility maximization problem serves not only as the mathematical foundation of consumer theory but as a metaphysical explanation of it as well.
If the template has a separate documentation page (usually called "Template:template name/doc"), add [[Category:Graph, chart and plot templates]] to the <includeonly> section at the bottom of that page. Otherwise, add <noinclude>[[Category:Graph, chart and plot templates]]</noinclude>
Advanced Placement (AP) Economics (also known as AP Econ) refers to two College Board Advanced Placement Program courses and exams addressing various aspects of the field of economics: AP Macroeconomics
The dotted line in red represents a cut with three crossing edges. The dashed line in green represents one of the minimum cuts of this graph, crossing only two edges. [1] In graph theory, a minimum cut or min-cut of a graph is a cut (a partition of the vertices of a graph into two disjoint subsets) that is minimal in some metric.
Under the standard assumption of neoclassical economics that goods and services are continuously divisible, the marginal rates of substitution will be the same regardless of the direction of exchange, and will correspond to the slope of an indifference curve (more precisely, to the slope multiplied by −1) passing through the consumption bundle in question, at that point: mathematically, it ...
A variant of the problem asks for a minimum weight k-cut where the output partitions have pre-specified sizes. This problem variant is approximable to within a factor of 3 for any fixed k if one restricts the graph to a metric space, meaning a complete graph that satisfies the triangle inequality . [ 7 ]