The correct path for the LSP, given the configuration and topological constraints, will exclude any link associated with the 'GREEN' admin group. Analyzing the diagram, the LSP will take the route with the lowest IGP metrics while avoiding 'GREEN' links. Starting from R1, the path with the lowest cumulative IGP metrics that also adheres to the exclusion of 'GREEN' links is through R1 -> R3 -> R2 -> R5 -> R4 -> R6. This results in R1, R3, R2, R5, R4, and R6 being the routers the LSP will traverse.