Abstract :
Numerous studies concerning the number and disposition of chordless paths on four vertices in graphs proved that there is a strong relation between these paths and the perfectness of graphs. In this paper, we further investigate this relation by introducing the notion of P4-domination and formulating two conjectures, which are used both to find an equivalent version of the odd pair conjecture and to frame it. In the last section, we prove some particular cases of these conjectures.
