A Nordhaus–Gaddum-type result is a (tight) lower or upper bound on the sum (or product) of a parameter of a graph and its complement. The path covering number c(G) of a graph is the smallest number of vertex-disjoint paths needed to cover the vertices of the graph. For two positive integers j and k with j ≥ k, an L( j, k)-labeling of a graph G is an… (More)