Stefan Dantchev
dantchev@dcs.qmul.ac.uk
(1) There is a resolution proof of the Weak Pigeon-Hole Principle, of size for any number of pigeons and any number of holes .
(2) Any resolution proof of of width has to be of size , independently from .
These results give not only a resolution size-width tradeoff for the Weak Pigeon-Hole Principle, but also almost optimal such trade-off for resolution in general. The upper bound (1) may be of independent interest, as it has been known for the two extreme values of , and , only.