The 3-extendability conjecture for bow-tie graphs

Let $C_m$ be a cycle of even length $m\ge6$, let $P_n$ be a path of odd order $n\ge5$, and let $C_m\bowtie P_n$ denote their bow-tie graph. 3-extendability conjecture. For any even integer $m\ge6$ and any odd integer $n\ge5$, the graph $C_m\bowtie P_n$ is $3$-extendable. This would provide an infinite family of $3$-extendable graphs with the stated bow-tie construction, extending the proved case involving $C_6\bowtie P_n$; the conjecture remains open in the source.