The completion conjecture for the graph invariant $c_2$

A graph's completion is the graph obtained by the completion operation referred to in the source, and $c_2$ denotes the $c_2$-invariant of a connected graph with at least three vertices. Completion conjecture. Graphs with identical completion have identical $c_2$. This is presented as a weaker version of the conjecture that equal periods imply equal $c_2$-invariants, and it has been tested on all primitive log-divergent $\phi^4$ graphs up to loop order $8$; its general validity remains open.