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We consider a stochastic matching model with a general compatibility graph,as introduced in \cite{MaiMoy16}. We show that the natural necessary conditionof stability of the system is also sufficient for the natural matching policy'First Come, First Matched' (FCFM). For doing so, we derive the stationarydistribution under a remarkable product form, by using an original dynamicreversibility property related to that of \cite{ABMW17} for the bipartitematching model.

A product form for the general stochastic matching model