A Note on Improved Bounds for the Oriented Radius of Mixed Multigraphs

ABSTRACT For an integer is the smallest value such that any 2‐edge connected mixed graph with a radius has an orientation with radius of no more than . In a recent significantly advancement, Babu, Benson, and Rajendraprasad showed that is at most . This finding is detailed in their paper “Improved bounds for the oriented radius of mixed multigraphs,” published in J. Graph Theory , 103 (2023), 674‐689. Furthermore, they proved that has an orientation with a radius of at most if every belongs to a cycle of length at most . The authors' results were derived through Observation 1, which served as the foundation for the development of Algorithm ORIENTOUT and Algorithm ORIENTIN. By integrating these algorithms, they obtained the improved bounds. However, an error has been identified in Observation 1, necessitating revisions to Algorithm ORIENTOUT and Algorithm ORIENTIN. In this note, we address the error and propose the necessary modifications to both algorithms, thereby ensuring the correctness of the conclusions.