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  • $\begingroup$ vc can be Max[Length@*Union /@ Transpose[ GraphEmbedding[ Graph[graph, GraphLayout -> "DiscreteSpiralEmbedding"]]]]? $\endgroup$ Commented May 8, 2017 at 2:09
  • $\begingroup$ @yode It was not clear to me if you are assuming that only edges can be deleted from the graph, or also vertices. If only edges are missing, then you can find the possible grid sizes like in here: mathematica.stackexchange.com/a/145440/12 $\endgroup$ Commented May 9, 2017 at 12:37
  • $\begingroup$ @yode, I think it's indeed the best answer so far. It can even accept symbolic vertices. As Szabolcs said, this is a (sub)isomorphism problem. It's a surprise that you didn't choose this as the accepted answer. $\endgroup$ Commented May 10, 2017 at 16:09
  • $\begingroup$ @UnchartedWorks Busy days, and I'm trying to make myself answer still. But I will always accept one answer. $\endgroup$ Commented May 10, 2017 at 16:23
  • $\begingroup$ @UnchartedWorks The problem with this answer is that it relies on an external tool. It cannot be used in Mathematica Online. kglr's answer is less efficient, but it uses only builtin functions. $\endgroup$ Commented May 10, 2017 at 16:52