turkmath.org

A matching in a graph $G$ is a set of independent edges in $G$. Graph matching has many applications in optimization, scheduling, and planning. A graph is called equimatchable if every maximal matching of it is a maximum matching. In other words, if every maximal matching in the graph has the same cardinality. Structure of equimatchable graphs is studied by several authors from different point of views; for example, in terms of having a perfect matching, or in terms of girth or connectivity. Equimatchable graphs with girth at least 5 is characterized, and here by giving a full characterization of triangle-free equimatchable graphs we extend this result. This is a joint work with Didem Gozupek and Yasemin Buyukcolak from Gebze Technical University.