Making Bidirected Graphs Strongly Connected

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.