A Bondy-type theorem for rainbow pancyclicity in graph systems

We establish a Hamiltonian-to-pancyclic analogue of Bondy's theorem for graph systems under an aggregate degree condition. Let $\G=(G_1,\ldots,G_n)$ be a graph system on a common $n$-vertex set $V$, and write $δ(v)=\min_{i\in[n]}d_{G_i}(v)$. If $\G$ contains a rainbow Hamilton cycle and \[ \sum_{v