We present a new technique for efficiently removing almost all short cycles in a graph
without unintentionally removing its triangles. Consequently, triangle finding problems do …

We study the approximability of two related problems on graphs with n nodes and m edges:
n-Pairs Shortest Paths (n-PSP), where the goal is to find a shortest path between O (n) …

We present several new efficient algorithms for approximating the girth, g, of weighted and
unweighted n-vertex, m-edge undirected graphs. For undirected graphs with polynomially …

Let G=(V, E, ℓ) be an-nodes m-edges weighted undirected graph, where ℓ: E→(0,∞) is a
real length function defined on its edges. Let g be the length of the shortest cycle in G. We …

Given an n-vertex m-edge graph G with nonnegative edge-weights, a shortest cycle is one
minimizing the sum of the weights on its edges. The girth of G is the weight of a shortest …

A graph is a mathematical construct that models pairwise relations between objects through
nodes (or vertices) and edges (also known as links) that connect these nodes. Due to the …