This paper presents a method for parsing  associative Lambek grammars based on graphtheoretic  properties. Connection graphs, which  are a simplified version of proof-nets, are  actually a mere conservative extension of the  earlier method of syntactic connexion,  discovered by Ajduckiewicz [1935]. The method  amounts to find alternating spanning trees in  graphs. A sketch of an algorithm for finding  such a tree is provided. Interesting properties of  time-complexity for this method are expected