## Pesquisa Operacional

*On-line version* ISSN 1678-5142

#### Abstract

CORTEZ MORALES, Walter Julio. **Uma caracterização de grafos imersíveis**.* Pesqui. Oper.* [online]. 2005, vol.25, n.1, pp.1-9.
ISSN 1678-5142. http://dx.doi.org/10.1590/S0101-74382005000100001.

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 n(G) the number of *edges* in a maximum *matching*, then there is a subset *X* Í *V*(*G*) such that |*V*(G)|+|*X*| - w(*G*\*X*) - 2n(* G*)=*0*, where w(*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 from 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.*

**Keywords
:
**graphs; immersible; complete antifactor; factorizable; Tutte-Berge's equation.