Rainbow Hamiltonian cycle conjecture for strongly edge-colored graphs

Let $G^c$ be a strongly edge-colored graph with $n$ vertices, where strongly edge-colored means that any two adjacent edges and any two edges joined by an edge have distinct colors. Its degree is the usual graph degree. Rainbow Hamiltonian cycle conjecture. Every strongly edge-colored graph $G^c$ with $n$ vertices and degree at least $\frac{n+1}{2}$ has a rainbow Hamiltonian cycle. This conjecture proposes a Dirac-type minimum-degree condition guaranteeing a rainbow Hamiltonian cycle in a strongly edge-colored graph; the source presents it as an open conjecture.