2025/12/11 by G. Arunkumar, Arunkumar, G., Samanta, Puja
Mathematics · Computer Science · #Graph theory and applications #Interconnection Networks and Systems #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.2512.10590
In a recent work, Sharma and Panda~\citesharma showed that every bipartite graph with a perfect matching has property (P). In this paper, we investigate the converse direction, i.e., when property (P) forces the existence of a perfect matching in bipartite graphs. We show that such graphs are balanced and establish that property (P) is equivalent to the existence of a perfect matching for several families of bipartite graphs.