A graph is balanced if its clique-vertex incidence matrix contains no square submatrix of odd order with exactly two ones per row and per column. There is a characterization of balanced graphs by forbidden induced subgraphs, ...

In this document, we study the scope of the following graph model: each vertex is assigned to a box in Rd and to a representative element that belongs to that box. Two vertices are connected by an edge if and only if its ...

We consider the following vertex-partition problem on graphs, known as the CLUSTER DELETION (CD) problem: given a graph with real nonnegative edge weights, partition the vertices into clusters (in this case, cliques) to ...

We prove that asymptotically (as n -> infinity) almost all graphs with n vertices and C(d)n(2-1/2d) log(1/d) n edges are universal with respect to the family of all graphs with maximum degree bounded by d. Moreover, we ...

The edge-intersection graph of a family of paths on a host tree is called an EPT graph. When the tree has maximum degree h, we say that the graph is [h,2,2]. If, in addition, the family of paths satisfies the Helly property, ...