The nature of the young and low-mass open clusters Pismis 5, vdB 80, NGC 1931 and BDSB 96

We investigate the nature of four young and low-mass open clusters (OCs) located in the second and third quadrants with near-infrared Two-Micron All Sky Survey (2MASS) photometry (errors < 0.1 mag). After field decontamination, the colour-magnitude diagrams (CMDs) display similar morphologies: a poorly populated main sequence (MS) and a dominant fraction of pre-MS (PMS) stars somewhat affected by differential reddening. Pismis 5, vdB 80 and BDSB 96 have MS ages within 5 +/- 4 Myr, while the MS of NGC 1931 is 10 +/- 3 Myr old. However, non-instantaneous star formation is implied by the wider (similar to 20 Myr) PMS age spread. The cluster masses derived from MS+PMS stars are low, within similar to 60-180 M-circle dot, with mass functions (MFs) significantly flatter than Salpeter's initial mass function (IMF). Distances from the Sun are within 1.0-2.4 kpc, and the visual absorptions are in the range A(V) = 1.0-2.0. From the stellar radial density profiles (RDPs), we find that they are small (R-c less than or similar to 0.48 pc, R-RDP less than or similar to 5.8 pc), especially Pismis 5 with R-c approximate to 0.2 pc and R-RDP approximate to 1.8 pc. Except for the irregular and cuspy inner regions of NGC 1931 and Pismis 5, the stellar RDPs follow a King-like profile. At similar to 10 Myr, central cusps - which in old clusters appear to be related to advanced dynamical evolution - are probably associated with a star formation and/or molecular cloud fragmentation effect. Despite the flat MFs, vdB 80 and BDSB 96 appear to be typical young, low-mass OCs. NGC 1931 and especially Pismis 5, with irregular RDPs, low cluster mass and flat MFs, do not appear to be in dynamical equilibrium. Both may be evolving into OB associations and/or doomed to dissolution in a few 10(7) yr.