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- W4933013 abstract "A configuration of the lit-only $sigma$-game on a finite graph $Gamma$ is an assignment of one of two states, on or off, to all vertices of $Gamma.$ Given a configuration, a move of the lit-only $sigma$-game on $Gamma$ allows the player to choose an on vertex $s$ of $Gamma$ and change the states of all neighbors of $s.$ Given any integer $k$, we say that $Gamma$ is $k$-lit if, for any configuration, the number of on vertices can be reduced to at most $k$ by a finite sequence of moves. Assume that $Gamma$ is a tree with a perfect matching. We show that $Gamma$ is 1-lit and any tree obtained from $Gamma$ by adding a new vertex on an edge of $Gamma$ is 2-lit." @default.
- W4933013 created "2016-06-24" @default.
- W4933013 creator A5034702725 @default.
- W4933013 date "2010-10-28" @default.
- W4933013 modified "2023-09-26" @default.
- W4933013 title "Lit-only sigma-game on some trees" @default.
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