Someone please correct me if I am wrong but I understood that part time working is written into UK employment law, and possibly European too?
I don't know about the employment law where you (OP) are, but obviously worth looking into.
Part time working is beneficial, in some cases essential, to employees to manage their child care or care of other dependants, and to be non discriminatory, it has to be offered to all employees. I don't think a company is obliged to allow all of its employees to work part time at once - just a percentage. In companies I have worked for, staff had to apply for part time working and get on a waiting list.