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This paper investigates the problem of multicast traffic grooming in transparent optical networks utilizing a grooming approach that is based on routing/grooming of multicast calls on hybrid graphs (HGs). HGs are constructed dynamically upon the arrival of each multicast call, in such a way that they are consisting of both the available physical links and the logical links with available free capacity. Two schemes for building the HGs are proposed, namely the minimum free capacity light-tree first (MCF) and the maximum free capacity light-tree first (MXCF), and also a novel hybrid Steiner tree (HST) heuristic for routing/grooming on HGs is presented. The proposed routing/grooming approach exhibits improved performance in terms of blocking probability compared to existing multicast grooming approaches that route/groom multicast calls by considering physical and logical links separately.