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Regular version of the site

Article

On the complexity of failed zero forcing

Theoretical Computer Science. 2017. Vol. 660. P. 102-104.
Shitov Y.

Let G be a simple graph whose vertices are partitioned into two subsets, called ‘filled’ vertices and ‘empty’ vertices. A vertex v is said to be forced by a filled vertex u if v is a unique empty neighbor of u. If we can fill all the vertices of G by repeatedly filling the forced ones, then we call an initial set of filled vertices a forcing set. We discuss the so-called failed forcing number of a graph, which is the largest cardinality of a set which is not forcing. Answering the recent question of Ansill, Jacob, Penzellna, Saavedra, we prove that this quantity is NP-hard to compute. Our proof also works for a related graph invariant which is called the skew failed forcing number.