Magnetic chains on superconducting systems have emerged as a platform for realization of Majorana bound states (MBSs) in condensed matter systems with possible applications to topological quantum computation. In this work we study the MBSs formed in magnetic chains on two-dimensional honeycomb materials with induced superconductivity. We establish phase diagrams showing the topological regions (where MBSs appear), which are strongly dependent on the spiral angle along the chain of the magnetic moments. In particular, find large regions where the topological phase is robust even at large values of the local Zeeman field, thus producing topological regions without an upper bound. Moreover, we show that the energy oscillations of the MBSs can show very different behavior with magnetic field strength. In some parameter regimes we find increasing oscillations amplitudes and decreasing periods, while in the other regimes the complete opposite behavior is found with increasing magnetic field strength. We also find that the topological phase can become dependent on the chain length, particularly in topological regions with a very high or no upper bound. In these systems we see a very smooth evolution from MBSs localized at chain end points to in-gap Andreev bound states spread over the full chain.
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