When Sciences Overlaps: A Matching Game under a Graph Concept

Initially, we provide basic knowledge of definitions and concepts related to the concept of matching in the graph. We are studying a model of games based on two players who take turns adding edges to this process eventually produces a maximal matching of the graph. We call the first Maximizer and second player Minimizer. The first aims to get a final matching to be large while the second one wants to reduce it. Maximizer wins if he manages a maximal matching while Minimizer wins if he can prevent him from doing this. The matcher number is the number of edges chosen when both players play optimally, while the matching number is the number of maximum matching edges. In this research we study the relationship between and . And we also prove some results on types of graph