An s-graph is a graph with two kind of edges: subdivisible edges and real edges. A realisation of an s-graph B is any graph obtained by subdividing subdivisible edges of B into pa...
Let H be a fixed graph on h vertices. We say that a graph G is induced H-free if it does not contain any induced copy of H. Let G be a graph on n vertices and suppose that at leas...
In the Connected Dominating Set problem we are given as input a graph G and a positive integer k, and are asked if there is a set S of at most k vertices of G such that S is a dom...
For a connected graph G = (V, E), a subset U ⊆ V is called a k-cut if U disconnects G, and the subgraph induced by U contains exactly k (≥ 1) components. More specifically, a ...
An r-component connected coloring of a graph is a coloring of the vertices so that each color class induces a subgraph having at most r connected components. The concept has been w...
Benny Chor, Michael R. Fellows, Mark A. Ragan, Igo...