I have two polygons, as below:
Does exist an automatic way to adjust the vertices of Pink Polygon near of Blue Polygon bounds to Blue Polygon bounds?
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With ArcGIS you can use the Snap tool, which will do exactly what you need but is only available with Standard and Advanced licences. If you don't have this licences, you could use integrate, but then you don't have the control on which vertex is moving. Note that both tools modify your data, so you better work on a copy of your dataset.