We use direct N -body simulations of gas embedded star clusters to study the importance of stellar collisions for the formation and mass accretion history of high-mass stars .
Our clusters start in virial equilibrium as a mix of gas and proto-stars .
Proto-stars then accrete matter using different mass accretion rates and the amount of gas is reduced in the same way as the mass of stars increases .
During the simulations we check for stellar collisions and we investigate the role of these collisions for the build-up of high-mass stars and the formation of runaway stars .

We find that a significant number of collisions only occur in clusters with initial half-mass radii r _ { h } \leq 0.1 pc .
After emerging from their parental gas clouds , such clusters end up too compact compared to observed young , massive open clusters .
In addition , collisions lead mainly to the formation of a single runaway star instead of the formation of many high mass stars with a broad mass spectrum .
We therefore conclude that massive stars form mainly by gas accretion , with stellar collisions only playing a minor role if any at all .
Collisions of stars in the pre-main sequence phase might however contribute to the formation of the most massive stars in the densest star clusters and possibly to the formation of intermediate-mass black holes with masses up to a few 100 M _ { \odot } .