A characterization of immersible graphs

This paper is motivated by the result of Berge who generalized Tutte's theorem which states that: Given a graph G with |V(G)| vertices and α(G) the number of edges in a maximum matching, then there is a subset X ∈ V(G) such that |V(G)|+|X| − β(G\X) − 2n(G)=0, where β(G\X) denotes the number of odd components of G\X, such expression is called Tutte–Berge's equation associated to G, denoted by T(G;X)=0. These graphs are then studied trom solutions of T(G;X)=0. A graph G is called immersible graph if and only if, its associated equation T(G;X)=0 has at least one non-emptyset for X, and it is non-immersible graph if and only if, the unique solution to T(G;X)=0 is the emptyset. The main result of this work is the characterization of immersible graphs via complete antifactor sets, moreover we prove that factorizable graphs are included in the class of immersible graphs.