Abstract
We define the (elementary) binary contraction G S of a graph G = ( V, E) in the following way: if 〈S 〉 is an induced K 1,2 not contained into an induced K 1,3, then G S is either the induced subgraph 〈VβS〉, or the graph obtained from 〈VβS〉 by adding a new vertex adjacent to those x ϵ VβS such that 〈 S ∪{ x}〉 has an odd number of edges (according that 〈S〉 is contained into an induced K 2,2 or not). We show that the binary contraction can be performed in some class of graphs such that: the line graphs, the subgraphs of a given root system (and thus the generalized line graphs), the subgraphs of L 1 (with a given scale and size), the graphs of negative type, ….
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