Polynomial-time computability of the core and corona in 2-bicritical graphs

Let $G$ be a $2$-bicritical graph with two odd cycles. The polynomial-time computability claim. The sets core $\core G$ and corona $\corona G$ can be computed in polynomial time. This proposes an algorithmic consequence of the structural results for $2$-bicritical graphs with two odd cycles; the source does not provide evidence that the claim has been proved or disproved.