On the complexity of failed zero forcing

  title={On the complexity of failed zero forcing},
  author={Yaroslav Shitov},
  journal={Theor. Comput. Sci.},
  • Y. Shitov
  • Published 1 September 2016
  • Mathematics, Computer Science
  • Theor. Comput. Sci.
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… 
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