Note: Minimum light number of lit-only σ-game on a tree

Authors:
Xinmao Wang;Yaokun Wu
Affiliations:
Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China;Department of Mathematics, Shanghai Jiao Tong University, Shanghai, 200240, China
Venue:
Theoretical Computer Science
Year:
2007

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Abstract

Let T be a tree with @? leaves. Each vertex of T is assigned a state either lit or off. An assignment of states to all the vertices of T is called a configuration. The lit-only @s-game allows the player to pick a lit vertex and change the states of all its neighbours. We prove that for any initial configuration one can make a sequence of allowable moves to arrive at a configuration in which the number of lit vertices is no greater than @?@?2@?. We also give examples to show that the bound @?@?2@? cannot be relaxed to @?@?2@?.