Tribonet explains why sharp knives are better than dull ones when it comes to cutting tomatoes. It's because dull knives are smooth so they can't grab the tomato skin to pull and tear it.
The easiest and safest way to slice a tomato is to use a sharp knife. The counterintuitive reason a sharp knife slices more easily through a tomato is that it has higher friction, albeit only on the knife's edge.
Slicing is actually stretching the tomato and, like most materials, a tomato is weaker when stretched than when compressed. Stretching the tomato skin creates a tearing force that opens a crack in the skin, thus beginning the slice.