Motivated by adjacency in perfect matching polytopes, we study the shortest reconfiguration problem of matchings via alternating cycles. Namely, want to find a sequence which transforms one given another such that symmetric difference each pair consecutive is single cycle. The equivalent combinatorial path polytopes. We prove NP-hard even when graph planar or bipartite, but it can be solved pol...

Determining the Fiedler vector of the Laplacian or adjacency matrices of graphs is the most computationally intensive component of several applications, such as graph partitioning, graph coloring, envelope reduction, and seriation. Often an approximation of the Fiedler vector is suÆcient. We discuss issues involved in the use of Monte Carlo techniques for this purpose.

Not long ago, Bagga, Beineke, and Varma [1] defined the super line multigraph of a simple graph Γ = (V,E) to be the graph Mr(Γ) whose vertex set is Pr(E), the class of r-element subsets of the edge set, and with an adjacency R ∼ R′ (where R,R′ ∈ Pr(E)) for every edge pair (e, f) with e ∈ R and f ∈ R′ such that e and f are adjacent in Γ. Thus, the number of edges joining R and R′ in Mr(Γ) is the...

Probability boxes, also called p-boxes, correspond to sets of probability distributions bounded by a pair distribution functions. They belong the class models known as imprecise probabilities. One central issues related probabilities is intervals values corresponding expectations random variables, and in particular interval bounds. In general, these are reached at extreme points credal sets, wh...

Let G be a graph with minimum degree δ. It is well-known that maximal adjacency orderings (MAOs) compute a vertex set S such that every pair of S is connected by at least δ internally vertex-disjoint paths in G. We present an algorithm that, given any pair of S, computes these δ paths in linear time O(n+m). This improves the previously best solutions for these special vertex pairs, which were f...