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The Full P-vertex Problem and Perfect Matchings for Bipartite Graphs
In a recent work, Sharma and Panda~\cite{sharma} showed that every bipartite graph with a perfect matching has property (P), and proved the converse for trees and unicyclic bipartite graphs (i.e., bipartite graphs with cycle rank $m(G) \le 1$). In this paper, we extend this result to broader classes
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