Decomposition of a bidirected graph into strongly connected components and its signed poset structure

Making Bidirected Graphs Strongly Connected

“…On the other hand, problems on bidirected graphs also have been considered in the literature. Ando, Fujishige and Nemoto [3] gave a linear-time algorithm for strongly connected component decomposition of bidirected graphs. This algorithm is made use of for the block triangularization of skew-symmetric matrices [11].…”

“…In this section, we introduce definitions and notation used in this paper. Definitions in this section mainly refer Ando and Fujishige [1] and Ando, Fujishige and Nemoto [3].…”

“…In Algorithm CONDENSE(G) described below, Steps 1-3 based on the steps of the strongly connected component decomposition algorithm of [3].…”

“…It is a common generalization of undirected graphs and directed graphs. For bidirected graphs, Ando, Fujishige and Nemoto [3] defined the notion of strong connectivity and gave a linear-time algorithm for the strongly connected component decomposition. However, problems to make a given bidirected graph strongly connected have not been formulated.…”

Bisubmodular polyhedra, simplicial divisions, and discrete convexity

“…Then we have a signed poset P(q) = (V, A(q)) that expresses the signed exchangeability associated with q for Q (see [1,2,6]). Signed poset P(q) has possible bidirected arcs a as follows:…”