OBS4 is supposed to be a list of all configurations which deny 4-colorability for themselves, and any strictly larger (in both dimensions) configurations.
Ie, if (19,17) is in OBS4 then (19+x,17+y) is not 4-colorable either. So given a shape (x,y) or even a more funky collection of grid points like a triangle, to know if it's 4-colorable just check for all X in OBS4, if you can fit X inside your shape.
Got it, although the more interesting property is that smaller shapes than those in OBS are 4-colorable? (because it is trivially true that if nxk cannot be colored then larger shapes can't either).
Right, he has apparently solved and proved a short list for OBS3 with the property that X is 3-colorable if and only if X doesn't contain anything from OBS3.
Ie, if (19,17) is in OBS4 then (19+x,17+y) is not 4-colorable either. So given a shape (x,y) or even a more funky collection of grid points like a triangle, to know if it's 4-colorable just check for all X in OBS4, if you can fit X inside your shape.