In this paper we give a fully dynamic approximation scheme for maintaining all-pairs shortest paths in planar networks. Given an error parameter ε such that 0 < ε, our algorit...
We present results related to satisfying shortest path queries on a planar graph stored in external memory. Let N denote the number of vertices in the graph and let sort(N) denote...
In this paper, we consider a number of results and six conjectures on properly coloured (PC) paths and cycles in edge-coloured multigraphs. We overview some known results and prov...
: A (directed) cycle C in a graph is called consistent provided there exists an automorphism of , acting as a 1-step rotation of C. A beautiful but not well-known result of J.H. Co...
For a graph G, let fij be the number of spanning rooted forests in which vertex j belongs to a tree rooted at i. In this paper, we show that for a path, the fij's can be expr...