We study the approximability of three versions of the Steiner tree problem. For the first one where the input graph is only supposed connected, we show that it is not approximable within better than | \ | for any ∊ ∈ (0, 1), where and are the vertex-set of the input graph and the set of...

Given a graph G and a positive integer K, the inverse chromatic number problem consists in modifying the graph as little as possible so that it admits a chromatic number not greater than K. In this paper, we focus on the inverse chromatic number problem for certain classes of graphs. First, we...