In this article, we present both structural and algorithmic questions on graphs, which are motivated by an application on Wi-Fi networks. In a CSMA/CA network, the fairness of each node is ensured when the subgraph induced by each channel is 1-extendable, i.e. each node belongs to a maximum independent set. We study two problems: the recognition of 1-extendable graphs, and then the assignation of channels such that each channel subgraph is 1-extendable. We propose not only theoretical answers (exact/approximation algorithms or hardness reductions) but also heuristics which allow us to output quickly a feasible solution for large instances.