Before revision:  We further investigate the relation between planar graphs and CPG graphs and show that CPG graphs are not necessarily planar and not all planar graphs are CPG . Our class generalizes the well studied class of VCPG graphs .
After revision:  Moreover, we investigate the recognition and 3-colorability problems for B_0-CPG, a subclass of CPG. We further show that CPG graphs are not necessarily planar and not all planar graphs are CPG . Our class generalizes the well studied class of VCPG graphs .