The New Sudoku Players' Forum

[bennys]

[tso]

This is called a "Nonrepetitive Path or Cycle".

See David Eppstien's paper:
Nonrepetitive Paths and Cycles in Graphs with Application to Sudoku

[bennys]

I will look into it.

[Lummox JR]

Another way to look at this is with the sort of inferences made by supercoloring. By propagating exclusions, you'll quickly find that not only are xy=x and xz=x mutually exclusive, but that the xy=y and xz=z are also mutually exclusive. From knowing that you can't have xy=y and xz=z together, you can eliminate anything intersecting xy=x and xz=x, which is all the x's on their entire row.

I'm sure the cycle is much easier to spot, though, at least where only 4 cells are concerned.