Symmetric Strategy in Graph Avoidance Games

Title: Symmetric Strategy in Graph Avoidance Games

Research Question: Can a symmetric strategy be developed for the second player in graph avoidance games, ensuring that the blue and red subgraphs are isomorphic regardless of the first player's strategy?

Methodology: The researchers studied the class of graphs G that admit a symmetric strategy for all forbidden graphs F. They discussed relevant graph-theoretic and complexity issues, as well as examples where a symmetric strategy may or may not exist.

Results: The researchers identified the class Csym of graphs G that have a symmetric strategy for the second player. They also found that Csym contains graphs with involutory automorphisms without fixed edges, such as even paths and cycles, bipartite complete graphs, and cubes.

Implications: The findings of this research have implications for the field of graph theory and game theory. The identification of graphs with a symmetric strategy provides a new approach to solving graph avoidance games and could lead to further advancements in these fields.

Conclusion: In conclusion, the researchers have developed a symmetric strategy for the second player in graph avoidance games, ensuring that the blue and red subgraphs are isomorphic regardless of the first player's strategy. This strategy can be applied to a class of graphs with involutory automorphisms without fixed edges. The research has implications for the fields of graph theory and game theory and could lead to further advancements in these areas.

Link to Article: https://arxiv.org/abs/0110049v1 Authors: arXiv ID: 0110049v1