We show how to use split decomposition to compute the weighted clique number and the chromatic number of a graph and we apply these results to some classes of graphs. In particular...
The vertex arboricity va(G) of a graph G is the minimum number of subsets into which the vertex set V (G) can be partitioned so that each subset induces an acyclic subgraph. The f...
A graph U is (induced)-universal for a class of graphs X if every member of X is contained in U as an induced subgraph. We study the problem of finding a universal graph with min...
The visibility graph V(X) of a discrete point set X R2 has vertex set X and an edge xy for every two points x, y X whenever there is no other point in X on the line segment betw...
In this paper we show that, if G is a Berge graph such that neither G nor its complement G contains certain induced subgraphs, named proper wheels and long prisms, then either G i...