Eliminate for polygons with shared vertices

Idea created by tomdilts on Oct 10, 2017

    It would be great if there were a version of the eliminate tool that could deal with polygons connected to other polygons only by one vertex. Currently the eliminate tool connects to polygons connected by two or more vertices.  When converting rasters to polygons it is really common to get polygons that are diagonal to one another (see the image below).