On total traffic domination in non-complete graphs

Abstract in Undetermined Given an undirected graph g(V, E), a set of traffic matrices H and one additional traffic matrix h, we say that H totally dominates h if, for each capacity reservation u supporting H, u also supports h using the same routing pattern. It has been shown that if vertical bar H vertical bar = 1 = (H = {(h) over cap}, say) and g, is a complete graph, H totally dominates h if, and only if, (h) over cap >= h component-wise. In this paper we give a generalized condition for vertical bar H vertical bar >= 1 and any undirected graph.