We study the effects of the environment on galaxy quenching in the outskirts of clusters at $0.04 < z < 0.08$. We use a subsample of 14 WINGS and OmegaWINGS clusters that are linked to other groups/clusters by filaments and study separately galaxies located in two regions in the outskirts of these clusters according to whether they are located towards the filaments directions or not. We also use samples of galaxies in clusters and field as comparison. Filamentary structures linking galaxy groups/clusters were identified over the Six Degree Field Galaxy Redshift Survey Data Release 3. We find a fraction of passive galaxies in the outskirts of clusters intermediate between that of the clusters and the fields. We find evidence of a more effective quenching in the direction of the filaments. We also analyse the abundance of post-starburst galaxies in the outskirts of clusters focusing our study on two extreme sets of galaxies according to their phase-space position: backsplash and true infallers. We find that up to $sim70%$ of post-starburst galaxies in the direction of filaments are likely backsplash, while this number drops to $sim40%$ in the isotropic infall region. The presence of this small fraction of galaxies in filaments that are falling into clusters for the first time and have been recently quenched, supports a scenario in which a significant number of filament galaxies have been quenched long time ago.
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