  We examine enthalpy relaxation across the chalcogenide glass series GexSe1-x,
prepared over close-by compositions using conventional melt-quenching
technique. We estimate the timescale {\tau}(Tg) characterizing enthalpic
relaxation near the kinetic glass transition temperature, using the
non-reversing heat-flow data obtained from MDSC (modulated differential
scanning calorimetry) measurements over a wide range of compositions (2.1
{\lessthanequalto} r {\lessthanequalto} 2.8, r = 2x+2). Anomalies in the
enthalpy-relaxation characteristic-times {\tau}g(r) are identified as marking
rigidity-transitions encountered in successive Ge-doping of polymeric selenium
chains.
