Perfect graphs form a well-known class of graphs introduced by Berge in the 1960s in terms of a min-max type equality involving two famous graph parameters. In this work, we survey certain variants and subclasses of perfect ...

© 2019 Elsevier B.V.Perfect graphs form a well-known class of graphs introduced by Berge in the 1960s in terms of a min–max type equality involving two famous graph parameters. In this work, we survey certain variants and ...

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, ...

Basic chordal graphs arose when comparing clique trees of chordal graphs and compatible trees of dually chordal graphs. They were defined as those chordal graphs whose clique trees are exactly the compatible trees of its ...

A biclique of a graph G is a maximal induced complete bipartite subgraph of G. The biclique graph of G, denoted by KB(G), is the intersection graph of the bicliques of G. We say that a graph G diverges (or converges or is ...

A graph is balanced if its clique-matrix contains no edge–vertex incidence matrix of an odd chordless cycle as a submatrix. While a forbidden induced subgraph characterization of balanced graphs is known, there is no such ...

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 ...

Circular-arc graphs are the intersection graphs of open arcs on a circle. Circle graphs are the intersection graphs of chords on a circle. These graph classes have been the subject of much study for many years and numerous ...

A new class of graphs related to perfect graphs is defined in this work: coordinated graphs. A graph G is coordinated if the cardinality of a maximum set of cliques of H with a common vertex is equal to the cardinality of ...