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Making Bidirected Graphs Strongly Connected

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Abstract

The problem of making a given directed graph strongly connected was well-investigated by Eswaran and Tarjan (SIAM J Comput 5:653–665, 1976). In contrast, the problem of making a given bidirected graph strongly connected has not yet been formulated. In this paper, we consider two related problems: making a given bidirected graph strongly connected with either the minimum cardinality of additional signs or the minimum cardinality of additional arcs. For the former problem, we show a closed formula of the minimum number of additional signs and give a linear-time algorithm for finding an optimal solution. For the latter problem, we give a linear-time algorithm for finding a feasible solution whose size is either equal to or more than the obvious lower bound by one.

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Acknowledgements

Both authors are supported by JSPS Research Fellowship for Young Scientists. The research of the first author was supported by JSPS KAKENHI Grant Number JP16J06879. Authors would like to thank the anonymous reviewer for the valuable comments.

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Correspondence to Tatsuya Matsuoka.

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Matsuoka, T., Sato, S. Making Bidirected Graphs Strongly Connected. Algorithmica 82, 787–807 (2020). https://doi.org/10.1007/s00453-019-00613-5

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  • DOI: https://doi.org/10.1007/s00453-019-00613-5

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