rostam/GraphTea

Sudoku 4x4

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In my opinion the regular graph with 16 vertices each of degree 7 is the model for the sudoku 4x4.
Therefore the chromatic number is 4 but GraphtTea says 6.
Who is right?
Thanks

Sorry, I am wrong: in the regular graph the vertices are not in the same order of Sudoku.
Instead, if I save this graph in GraphTea format, when I load it it looses some edges ...