Proceedings 32nd Annual Symposium of Foundations of Computer Science (1991)
San Juan, Puerto Rico
Oct. 1, 1991 to Oct. 4, 1991
H.N. Gabow , Dept. of Comput. Sci., Colorado Univ., Boulder, CO, USA
A poset representation for a family of sets defined by a labeling algorithm is investigated. Poset representations are given for the family of minimum cuts of a graph, and it is shown how to compute them quickly. The representations are the starting point for algorithms that increase the edge connectivity of a graph, from lambda to a given target tau = lambda + delta , adding the fewest edges possible. For undirected graphs the time bound is essentially the best-known bound to test tau -edge connectivity; for directed graphs the time bound is roughly a factor delta more. Also constructed are poset representations for the family of rigid subgraphs of a graph, when graphs model structures constructed from rigid bars. The link between these problems is that they all deal with graphic matroids.
graphic matroids, poset representation, edge connectivity, graph rigidity, labeling algorithm, minimum cuts, undirected graphs, time bound, directed graphs, rigid subgraphs, rigid bars
H. Gabow, "Applications of a poset representation to edge connectivity and graph rigidity,"  Proceedings 32nd Annual Symposium of Foundations of Computer Science(FOCS), San Juan, Puerto Rico, 1991, pp. 812-821.