3 ms·
It's a counterexample to "if and only if".
by sp332 4y ago
It's a counterexample to "if and only if".
- thaumasiotes 4y agoDo you know what "if and only if" means? If the diamond can be colored using the checkerboard pattern, then it is not a counterexample to the iff-qualified statement, because it is true that "you can packing-color the graph [while] enforcing the checkerboard pattern of 1s". The graph is 14-colorable and it is 14-colorable with a checkerboard pattern of 1s; both claims are true and the iff is satisfied. Note that the "only if" direction of this conjecture is the only meaningful one; in the "if" direction, you have "if you can k-color a graph while obeying a particular coloring constraint, then you can k-color the graph", which is obvious.