Let G be the graph whose vertices are the 1225 squares of a square board with 35 rows and 35 columns. Two vertices are neighbors if placing a dame in each of the lockers the ladies attack each other. (That is, if the boxes are in the same row, column or diagonal, where diagonal is not necessarily one of the main diagonals). Prove that χ (G) = 35.

Dame is equivalent to a queen in English.