Lifetimes of the excited states in the neutron-rich Ti-52,Ti-54 nuclei, produced in a multinucleon-transfer reaction, were measured by employing the Cologne plunger device and the recoil-distance Doppler-shift method. The experiment was performed at the Grand Accelerateur National d'Ions Lourds facility by using the Advanced Gamma Tracking Array for the gamma-ray detection, coupled to the large-acceptance variable mode spectrometer for an event-by-event particle identification. A comparison between the transition probabilities obtained from the measured lifetimes of the 2(1)(+) to 8(1)(+) yrast states in Ti-52,Ti-54 and that from the shell-model calculations based on the well-established GXPF1A, GXPF1B, and KB3G fp shell interactions support the N = 32 subshell closure. The B(E2) values for Ti-52 determined in this work are in disagreement with the known data, but are consistent with the predictions of the shell-model calculations and reduce the previously observed pronounced staggering across the even-even titanium isotopes.