Sudoku & Graph Theory.

This article examines the chain exclusion and pile exclusion rules for solving Sudoko logic puzzles. The goal of the logical Sudoko solver is to prove that only one possible number can be assigned to each vertex and to find that number for each vertex in which the number is not defined. The possible numbers that should be assigned to a row, column or one of the nine 3x3 subsquares as a permutation bipartite graph or nodes. A number can only be assigned to a vertex that contains the possibility of assigning that number. Pile exclusion and chain exclusion provide the basis of logical elimination rules.