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ChildClassName childSpecificName = new ChildCLassName(this);

|| OR ||

public partial class ParentClassName
{
  private ChildClassName _childSpecificName;

  public ParentClasName()
  {
    _childSpecificName = new ChildCLassName(this);
  }
}

public partial class ChildClassName
{
  private ParentClassName _parent;

  public ChildClasName(ParentClassName parent)
  {
    _parent = parent;
  }
}