We extend the basic theory concerning the cycle space of a finite graph to infinite locally finite graphs, using as infinite cycles the homeomorphic images of the unit circle in t...
Let G = (V; E; w) be an undirected graph with nonnegative edge length function w and nonnegative vertex weight function r. The optimal product-requirement communication spanning t...
Given a graph G and a spanning tree T of G, we say that T is a tree t-spanner of G if the distance between every pair of vertices in T is at most t times their distance in G. The p...
It has long been known that the number of spanning trees in circulant graphs with fixed jumps and n nodes satisfies a recurrence relation in n. The proof of this fact was algebra...
For a connected graph G, let L(G) denote the maximum number of leaves in a spanning tree in G. The problem of computing L(G) is known to be NP-hard even for cubic graphs. We improv...