On local and global independence numbers of a graph Original Research Article

The local independence number αi(G) of a graph G at a distance i is the maximum number of independent vertices at distance i from any vertex. We study the impact of restricting αi(G) on the (global) independence number α(G). Among others, we show that in graphs with bounded diameter, α(G) is bounded if and only if αi(G) is bounded for at least one i, 2⩽i⩽(diam(G)−1)/4.