Menu
Two quasigroup identities of importance in combinatorics, Schröder’s Second Law and Stein’s Third Law, share many common features that are incorporated under the guise of palindromic quasigroups. A graph-theoretical technique yields a topological proof for the congruence restrictions on the spectrum of Schröder or outer palindromic quasigroups. The potential for a comparable proof applicable to Stein or inner palindromic quasigroups raises open graph-theoretical and combinatorial problems. Imposition of extra Sudoku-like conditions on Latin squares of square order, based on the coloring of so-called Sudoku graphs, leads to the concept of a Sudoku quasigroup. It is shown that the spectrum of inner palindromic Sudoku quasigroups comprises every perfect square, thereby identifying the chromatic number of each Sudoku graph.