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  2. Mathematical puzzle - Wikipedia

    en.wikipedia.org/wiki/Mathematical_puzzle

    Mathematical puzzles require mathematics to solve them. Logic puzzles are a common type of mathematical puzzle. Conway's Game of Life and fractals, as two examples, may also be considered mathematical puzzles even though the solver interacts with them only at the beginning by providing a set of initial conditions. After these conditions are set ...

  3. Graph coloring game - Wikipedia

    en.wikipedia.org/wiki/Graph_coloring_game

    The graph coloring game is a mathematical game related to graph theory. Coloring game problems arose as game-theoretic versions of well-known graph coloring problems. In a coloring game, two players use a given set of colors to construct a coloring of a graph, following specific rules depending on the game we consider.

  4. Five-room puzzle - Wikipedia

    en.wikipedia.org/wiki/Five-room_puzzle

    If the solution line starts somewhere else, the observer will see the solution line enter and leave (two walls), enter and leave a second time (two more walls) and finally enter through the fifth wall and end (all five walls have been crossed, so the line cannot get back out of the room again).

  5. Graph theory - Wikipedia

    en.wikipedia.org/wiki/Graph_theory

    The works of Ramsey on colorations and more specially the results obtained by Turán in 1941 was at the origin of another branch of graph theory, extremal graph theory. The four color problem remained unsolved for more than a century. In 1969 Heinrich Heesch published a method for solving the problem using computers. [29]

  6. List of NP-complete problems - Wikipedia

    en.wikipedia.org/wiki/List_of_NP-complete_problems

    Graph homomorphism problem [3]: GT52 Graph partition into subgraphs of specific types (triangles, isomorphic subgraphs, Hamiltonian subgraphs, forests, perfect matchings) are known NP-complete. Partition into cliques is the same problem as coloring the complement of the given graph. A related problem is to find a partition that is optimal terms ...

  7. Five color theorem - Wikipedia

    en.wikipedia.org/wiki/Five_color_theorem

    If the graph is empty, we go to the final step 5 below. Otherwise, Wernicke's Theorem tells us that S 5 is nonempty. Pop v off S 5 , delete it from the graph, and let v 1 , v 2 , v 3 , v 4 , v 5 be the former neighbors of v in clockwise planar order, where v 1 is the neighbor of degree at most 6.

  8. Longest path problem - Wikipedia

    en.wikipedia.org/wiki/Longest_path_problem

    In graph theory and theoretical computer science, the longest path problem is the problem of finding a simple path of maximum length in a given graph.A path is called simple if it does not have any repeated vertices; the length of a path may either be measured by its number of edges, or (in weighted graphs) by the sum of the weights of its edges.

  9. Assignment problem - Wikipedia

    en.wikipedia.org/wiki/Assignment_problem

    This is an unbalanced assignment problem. One way to solve it is to invent a fourth dummy task, perhaps called "sitting still doing nothing", with a cost of 0 for the taxi assigned to it. This reduces the problem to a balanced assignment problem, which can then be solved in the usual way and still give the best solution to the problem.

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