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- W3100194708 abstract "An irreversible $k$-threshold process (also a $k$-neighbor bootstrappercolation) is a dynamic process on a graph where vertices change color fromwhite to black if they have at least $k$ black neighbors. An irreversible$k$-conversion set of a graph $G$ is a subset $S$ of vertices of $G$ such thatthe irreversible $k$-threshold process starting with $S$ black eventuallychanges all vertices of $G$ to black. We show that deciding the existence of anirreversible 2-conversion set of a given size is NP-complete, even for graphsof maximum degree 4, which answers a question of Dreyer and Roberts.Conversely, we show that for graphs of maximum degree 3, the minimum size of anirreversible 2-conversion set can be computed in polynomial time. Moreover, wefind an optimal irreversible 3-conversion set for the toroidal grid,simplifying constructions of Pike and Zou." @default.
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- W3100194708 date "2014-12-13" @default.
- W3100194708 modified "2023-09-26" @default.
- W3100194708 title "Irreversible 2-conversion set in graphs of bounded degree" @default.
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