In space division multiplexing-elastic optical networks (SDM-EONs), crosstalk and fragmentation are the significant factors determining overall resource utilization. Crosstalk and fragmentation management spectral resource allocation schemes can enhance the overall resource utilization in SDM-EONs. This paper proposes three crosstalk and fragmentation management bi-directional resource allocation schemes for multi-core SDM-EONs to suppress inter-core crosstalk and network fragmentation. A spatial resource partitioning method is presented to mitigate inter-core crosstalk, and this paper adopts a k-shortest path routing method to suppress fragmentation while spectral resource allocation. To the best of our knowledge, there is no such scheme that handles both crosstalk and fragmentation together while allocating spectral resources in a counter-propagating manner for multi-core fiber (MCF) SDM-EONs. The estimated result shows that the proposed scheme outperforms the traditional co-propagation method and enhances existing resource utilization by reducing blocked requests.