What does "Connectivity Game" mean?

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A connectivity game involves two players who take turns on a graph made up of nodes (points) and edges (connections between points). The goal for one player is to visit every node in the graph infinitely often.

In this game, one player is trying to cover all the nodes, while the other player tries to block them. The games are played on a special type of graph called a bipartite graph, where the nodes can be split into two separate groups. The connections only happen between these two groups, not within them.

Solving these games can help with other types of games, especially those used in checking systems for correctness. By using smart strategies and algorithms, players can improve their chances of winning by making efficient moves.

Researchers have found that figuring out how to win these connectivity games relates closely to another problem called maintaining strongly connected components in a graph. This is important in the field of graph theory and computer science. New algorithms have been created to help solve these games better and faster than before, making the overall game-play experience more efficient.