This paper proves a necessary and sufficient condition for the existence of iterative algorithms that achieve approximate Byzantine consensus in arbitrary directed graphs, where e...
We consider the reachability problem for a certain class of directed acyclic graphs embedded on surfaces. Let G(m, g) be the class of directed acyclic graphs with m = m(n) source ...
Let (G) denote the domination number of a graph G and let G H denote the Cartesian product of graphs G and H. We prove that (G)(H) 2(G H) for all simple graphs G and H. 2000 Math...
Since the advent of electronic computing, the processors’ clock speed has risen tremendously. Now that energy efficiency requirements have stopped that trend, the number of proc...
We consider a class of routing problems on connected graphs G. Initially, each vertex v of G is occupied by a “pebble” which has a unique destination π(v) in G (so that π is...