We present a method for reducing the treewidth of a graph while preserving all the minimal s−t separators. This technique turns out to be very useful in the design of parameteriz...
Consider the following problem: For given graphs G and F1, . . . , Fk, find a coloring of the edges of G with k colors such that G does not contain Fi in color i. For example, if e...
We present an O(m + n)-time algorithm that tests if a given directed graph is 2-vertex connected, where m is the number of arcs and n is the number of vertices. Based on this resul...
Given a stable marriage problem instance represented by a bipartite graph having 2n vertices and m edges, we describe an algorithm that can verify the stability of k different mat...
A graph is Y Y reducible if it can be reduced to isolated vertices by a sequence of series-parallel reductions and Y Y transformations. It is still an open problem to characterize...