Frustrated Alternating Tree
# Definition
Suppose $G$ is an Undirected Graph, $M$ is a Matching on $G$, and $(T, r)$ is an $M$-alternating tree. We say $T$ is a Frustrated Alternating Tree if $\forall e \in E(G)$ s.t. $e \cap B(T) \neq \emptyset$, we have that $e \cap A(T) \neq \emptyset$. That is, each Graph Edge with a endpoint in $B(T)$ has its other endpoint in $A(T)$.