3 research outputs found
The Complexity of Node Blocking for Dags
We consider the following modification of annihilation game called node
blocking. Given a directed graph, each vertex can be occupied by at most one
token. There are two types of tokens, each player can move his type of tokens.
The players alternate their moves and the current player selects one token
of type and moves the token along a directed edge to an unoccupied vertex.
If a player cannot make a move then he loses. We consider the problem of
determining the complexity of the game: given an arbitrary configuration of
tokens in a directed acyclic graph, does the current player has a winning
strategy? We prove that the problem is PSPACE-complete.Comment: 7 pages, 3 figure
Minimum Light Numbers in the -Game and Lit-Only -Game on Unicyclic and Grid Graphs
Consider a graph each of whose vertices is either in the ON state or in the OFF state and call the resulting ordered bipartition into ON vertices and OFF vertices a configuration of the graph. A regular move at a vertex changes the states of the neighbors of that vertex and hence sends the current configuration to another one. A valid move is a regular move at an ON vertex. For any graph let be the minimum integer such that given any starting configuration of there must exist a sequence of valid moves which takes to a configuration with at most ON vertices provided there is a sequence of regular moves which brings to a configuration in which there are ON vertices. The shadow graph of a graph is obtained from by deleting all loops. We prove that if is unicyclic and give an example to show that the bound is tight. We also prove that if is a two-dimensional grid graph and if is a two-dimensional grid graph but not a path and