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  2. Scheinerman's conjecture - Wikipedia

    en.wikipedia.org/wiki/Scheinerman's_conjecture

    In mathematics, Scheinerman's conjecture, now a theorem, states that every planar graph is the intersection graph of a set of line segments in the plane. This conjecture was formulated by E. R. Scheinerman in his Ph.D. thesis , following earlier results that every planar graph could be represented as the intersection graph of a set of simple curves in the plane (Ehrlich, Even & Tarjan 1976).

  3. P versus NP problem - Wikipedia

    en.wikipedia.org/wiki/P_versus_NP_problem

    They are some of the very few NP problems not known to be in P or to be NP-complete. The graph isomorphism problem is the computational problem of determining whether two finite graphs are isomorphic. An important unsolved problem in complexity theory is whether the graph isomorphism problem is in P, NP-complete, or NP-intermediate.

  4. List of unsolved problems in mathematics - Wikipedia

    en.wikipedia.org/wiki/List_of_unsolved_problems...

    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.

  5. Shortest path problem - Wikipedia

    en.wikipedia.org/wiki/Shortest_path_problem

    The all-pairs shortest path problem finds the shortest paths between every pair of vertices v, v' in the graph. The all-pairs shortest paths problem for unweighted directed graphs was introduced by Shimbel (1953), who observed that it could be solved by a linear number of matrix multiplications that takes a total time of O(V 4).

  6. Intersection graph - Wikipedia

    en.wikipedia.org/wiki/Intersection_graph

    An example of how intersecting sets define a graph. In graph theory, an intersection graph is a graph that represents the pattern of intersections of a family of sets.Any graph can be represented as an intersection graph, but some important special classes of graphs can be defined by the types of sets that are used to form an intersection representation of them.

  7. De Morgan's laws - Wikipedia

    en.wikipedia.org/wiki/De_Morgan's_laws

    De Morgan's laws represented with Venn diagrams.In each case, the resultant set is the set of all points in any shade of blue. In propositional logic and Boolean algebra, De Morgan's laws, [1] [2] [3] also known as De Morgan's theorem, [4] are a pair of transformation rules that are both valid rules of inference.

  8. Intersection (geometry) - Wikipedia

    en.wikipedia.org/wiki/Intersection_(geometry)

    This proves that all points in the intersection are the same distance from the point E in the plane P, in other words all points in the intersection lie on a circle C with center E. [5] This proves that the intersection of P and S is contained in C. Note that OE is the axis of the circle. Now consider a point D of the circle C. Since C lies in ...

  9. Forbidden graph characterization - Wikipedia

    en.wikipedia.org/wiki/Forbidden_graph...

    A prototypical example of this phenomenon is Kuratowski's theorem, which states that a graph is planar (can be drawn without crossings in the plane) if and only if it does not contain either of two forbidden graphs, the complete graph K 5 and the complete bipartite graph K 3,3.

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