Abstract:A configuration of a graph is an assignment of one of two states, on or off, to each vertex of it. A regular move at a vertex changes the states of the neighbors of that vertex. A valid move is a regular move at an on vertex. The following result is proved in this note: given any starting configuration x of a tree, if there is a sequence of regular moves which brings x to another configuration in which there are ℓ on vertices then there must exist a sequence of valid moves which takes x to a configuration with… Show more
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