The link between gas and stars in the S254-S258 star-forming region
  The paper aims to study relation between the distributions of the young
stellar objects (YSOs) of different ages and the gas-dust constituents of the
S254-S258 star-formation complex. This is necessary to study the time evolution
of the YSO distribution with respect to the gas and dust compounds which are
responsible for the birth of the young stars. For this purpose we use
correlation analysis between different gas, dust and YSOs tracers. We compared
the large-scale CO, HCO$^+$, near-IR extinction, and far-IR {\it Herschel} maps
with the density of YSOs of the different evolutionary Classes. The direct
correlation analysis between these maps was used together with the
wavelet-based spatial correlation analysis. This analysis reveals a much
tighter correlation of the gas-dust tracers with the distribution of Class I
YSOs than with that of Class II YSOs. We argue that Class I YSOs which were
initially born in the central bright cluster S255-IR (both N and S parts)
during their evolution to Class II stage ($\sim$2 Myr) had enough time to
travel through the whole S254-S258 star-formation region. Given that the region
contains several isolated YSO clusters, the evolutionary link between these
clusters and the bright central S255-IR (N and S) cluster can be considered.
Despite the complexity of the YSO cluster formation in the non-uniform medium,
the clusters of Class II YSOs in the S254-258 star-formation region can contain
objects born in the different locations of the complex.
