Graphs with Large Maximum Forcing Number

This paper investigates the maximum forcing number of graphs, a concept related to perfect matchings. It confirms a conjecture by Liu and Zhang, providing a bound on the maximum forcing number based on the number of edges. The paper also explores the relationship between the maximum forcing number and matching switches in bipartite graphs, and investigates the minimum forcing number in specific cases. The results contribute to the understanding of graph properties related to matchings and forcing numbers.