On total traffic domination in non-complete graphs

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 |H|=1 (H={hˆ}, say) and G is a complete graph, H totally dominates h if, and only if, hˆ≥h component-wise. In this paper we give a generalized condition for |H|≥1 and any undirected graph.