We perform the largest currently available set of direct N-body calculations of young star cluster models to study the dynamical influence, especially through the ejections of the most massive star in the cluster, on the current relation between the maximum-stellar-mass and the star-cluster-mass. We vary several initial parameters such as the initial half-mass radius of the cluster, the initial binary fraction, and the degree of initial mass segregation. Two different pairing methods are used to construct massive binaries for more realistic initial conditions of massive binaries. We find that lower mass clusters (= 1000 Msun), no most-massive star escapes the cluster within 3 Myr regardless of the initial conditions if clusters have initial half-mass radii, r_0.5, >= 0.8 pc. However, a few of the initially smaller sized clusters (r_0.5 = 0.3 pc), which have a higher density, eject their most massive star within 3 Myr. If clusters form with a compact size and their massive stars are born in a binary system with a mass-ratio biased towards unity, the probability that the mass of the most massive star in the cluster changes due to the ejection of the initially most massive star can be as large as 20 per cent. Stellar collisions increase the maximum-stellar-mass in a large number of clusters when clusters are relatively dense (M_ecl >= 10^3 Msun and r_0.5 = 0.3 pc) and binary-rich. Overall, we conclude that dynamical effects hardly influence the observational maximum-stellar-mass — cluster mass relation.