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Twenty six
According to this wikipedia article there have been twenty six wars in Europe during the period of Pax Europaea. Below is a list of them.
Upvote:7
Here is a timeline I recently made of conflicts after the WWII in Europe including Russian involvement. Size is according to deaths. Color, according to nature of the conflict. The Bosnian War was harsh (95k deaths), but much so the Greek Civil War (190k deaths). Also worth mentioning the 2nd Chechen war (75k deaths). The Czechoslovakia Invasion (300 deaths) pales in comparizon to the little known Baltic Resistance (35k deaths) to soviets, and also to the Spanish Maquis (6,5k deaths) is neglected often.
The majority of these conflicts are on the periphery of Europe. In fact, Western Europe only has had some minor conflicts. In addition, many of the conflicts were part of the Cold War.
We could debate the frontiers of Europe and add colonial conflicts and international interventions, but I think this is not the point. The Russo-Georgian war was very much an European war, but decolonization wars were not. In fact, what you see is that Russia is involved in many, many of the conflicts in Europe. What's more important, Russia seems to be involved in European conflicts non-stop, excluding the latter Soviet years when they were unable to do much except for Afghanistan.