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Microsoft Math Solver (formerly Microsoft Mathematics and Microsoft Math) is an entry-level educational app that solves math and science problems.Developed and maintained by Microsoft, it is primarily targeted at students as a learning tool.
The illustration on the right shows a maximum cut: the size of the cut is equal to 5, and there is no cut of size 6, or |E| (the number of edges), because the graph is not bipartite (there is an odd cycle). In general, finding a maximum cut is computationally hard. [3] The max-cut problem is one of Karp's 21 NP-complete problems. [4]
In any graph without isolated vertices, the sum of the matching number and the edge covering number equals the number of vertices. [5] If there is a perfect matching, then both the matching number and the edge cover number are |V | / 2. If A and B are two maximal matchings, then |A| ≤ 2|B| and |B| ≤ 2|A|.
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
An algorithm is fundamentally a set of rules or defined procedures that is typically designed and used to solve a specific problem or a broad set of problems.. Broadly, algorithms define process(es), sets of rules, or methodologies that are to be followed in calculations, data processing, data mining, pattern recognition, automated reasoning or other problem-solving operations.
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For a graph G, let χ(G) denote the chromatic number and Δ(G) the maximum degree of G.The list coloring number ch(G) satisfies the following properties.. ch(G) ≥ χ(G).A k-list-colorable graph must in particular have a list coloring when every vertex is assigned the same list of k colors, which corresponds to a usual k-coloring.
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