Experts and BHG readers answer.
Violets can be very tenacious weeds, especially where the soil is compacted, acid and in damp shade. Violets are interesting in that they have two methods of seed-producion, which results in huge numbers of seeds. If you mow or dig them at bloom time, you will remove leaves but only the seeds that are produced by the flowers. However violets also produce another crop of seeds without visible flowers later in the season. These are produced at or below ground level and are hard to see. The best thing is to dig as many plants as you can and remove them, roots and all, in the spring. If any sprout afterwards, dig these out as well. Do this conscientiously for several years and you will gradually win the battle.