Abstract
Let \(\mu (N,v,L)\) be the Myerson value for graph games (N, v, L). We call a link ij of a graph L safe if \(\mu _k(N,v,L)\ge \mu _k(N,v,L\setminus \{ij\})\) for any \(k\in N\), which means that none of players benefits from breaking the link ij. A link \(ij\in L\) is called a bridge if N splits into more components after ij is deleted. We show that if (N, v) is convex, then any bridge is safe. Furthermore, if (N, v) is strictly convex, then a link is safe if and only if it is a bridge.
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Acknowledgements
We are grateful to the Editor Professor Psarras and the referees for invaluable comments and suggestions that improve the results and presentations substantially, in which one of referees proposed the problem in Conclusions. This research was partially supported by the National Natural Science Foundation of China (No. 11971298).
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This research was partly supported by NSFC (No. 11971298)
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Li, D.L., Shan, E. Safety of links with respect to the Myerson value for communication situations. Oper Res Int J 22, 2121–2131 (2022). https://doi.org/10.1007/s12351-020-00602-5
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DOI: https://doi.org/10.1007/s12351-020-00602-5