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Definition: A $\textit{matching}$ in a graph $G$ is a subgraph consisting of pairwise disjoint edges. If the subgraph is an induced subgraph, the matching is an $\textit{induced matching}$. The largest size of an induced matching in $G$ is called its induced matching number and denoted by $a(G)$.

Let $G$ be a bipartite graph. Is it possible to characterize the set of vertices $x$ of $G$ such that $a(G \setminus x)<a(G)$ ?

Definition: A matching in a graph $G$ is a subgraph consisting of pairwise disjoint edges. If the subgraph is an induced subgraph, the matching is an induced matching. The largest size of an induced matching in $G$ is called its induced matching number and denoted by $a(G)$.

Let $G$ be a bipartite graph. Is it possible to characterize the set of vertices $x$ of $G$ such that $a(G \setminus x)<a(G)$ ?

Definition: A $\textit{matching}$ in a graph $G$ is a subgraph consisting of pairwise disjoint edges. If the subgraph is an induced subgraph, the matching is an $\textit{induced matching}$. The largest size of an induced matching in $G$ is called its induced matching number and denoted by $a(G)$.

Let $G$ be a bipartite graph. Is it possible to characterize the vertex $x$ such that $a(G \setminus x)<a(G)$ ?

Definition: A $\textit{matching}$ in a graph $G$ is a subgraph consisting of pairwise disjoint edges. If the subgraph is an induced subgraph, the matching is an $\textit{induced matching}$. The largest size of an induced matching in $G$ is called its induced matching number and denoted by $a(G)$.

Let $G$ be a bipartite graph. Is it possible to characterize the set of vertices $x$ of $G$ such that $a(G \setminus x)<a(G)$ ?

Definition: A $\textit{matching}$ in a graph $G$ is a subgraph consisting of pairwise disjoint edges. If the subgraph is an induced subgraph, the matching is an $\textit{induced matching}$. The largest size of an induced matching in $G$ is called its induced matching number and denoted by $a(G)$.

Let $G$ be a bipartite graph. Is it possible to characterize the vertex $x$ such that $a(G \setminus x)<a(G)$ ?

Thanks in advance.

Definition: A $\textit{matching}$ in a graph $G$ is a subgraph consisting of pairwise disjoint edges. If the subgraph is an induced subgraph, the matching is an $\textit{induced matching}$. The largest size of an induced matching in $G$ is called its induced matching number and denoted by $a(G)$.

Let $G$ be a bipartite graph. Is it possible to characterize the vertex $x$ such that $a(G \setminus x)<a(G)$ ?