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A graph coloring of the Sudoku graph using this number of colors (the minimum possible number of colors for this graph) can be interpreted as a solution to the puzzle. The usual form of a Sudoku puzzle, in which some cells are filled in with symbols and the rest must be filled in by the person solving the puzzle, corresponds to the precoloring ...
A proper vertex coloring of the Petersen graph with 3 colors, the minimum number possible. In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. In its simplest form, it is a way of coloring the vertices of a graph ...
Mathematical context. The general problem of solving Sudoku puzzles on n2 × n2 grids of n × n blocks is known to be NP-complete. [8] A puzzle can be expressed as a graph coloring problem. [9] The aim is to construct a 9-coloring of a particular graph, given a partial 9-coloring. The Sudoku graph has 81 vertices, one vertex for each cell.
Taking Sudoku Seriously. Taking Sudoku Seriously: The math behind the world's most popular pencil puzzle is a book on the mathematics of Sudoku. It was written by Jason Rosenhouse and Laura Taalman, and published in 2011 by the Oxford University Press. The Basic Library List Committee of the Mathematical Association of America has suggested its ...
A Sudoku puzzle can be expressed as a graph coloring problem. [30] The aim is to construct a 9-coloring of a particular graph, given a partial 9-coloring. The fewest clues possible for a proper Sudoku is 17. [31] Tens of thousands of distinct Sudoku puzzles have only 17 clues. [32]
Sudoku solving algorithms. A typical Sudoku puzzle. A standard Sudoku contains 81 cells, in a 9×9 grid, and has 9 boxes, each box being the intersection of the first, middle, or last 3 rows, and the first, middle, or last 3 columns. Each cell may contain a number from one to nine, and each number can only occur once in each row, column, and box.
Graph coloring [2] [3]: GT4 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.
To transform a precoloring extension problem into a list coloring problem, assign each uncolored vertex in the precoloring extension problem a list of the colors not yet used by its initially-colored neighbors, and then remove the colored vertices from the graph. Sudoku puzzles may be modeled mathematically as instances of the precoloring ...
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