Biró et al. (Discrete. Math 100(1–3):267–279, 1992) introduced the concept of H-graphs, intersection graphs connected subgraphs a subdivision graph H. They are related to and generalize many important classes geometric graphs, e.g., interval circular-arc split chordal graphs. Our paper starts new line research in area by studying several classical computational problems on H-graphs: recognition...

Random intersection graphs model networks with communities, assuming an underlying bipartite structure of groups and individuals, where these may overlap. Group memberships are generated through the configuration model. Conditionally on group memberships, classical random graph is obtained by connecting individuals when they together in at least one group. We generalize this definition, allowin...

Abstract: The intersection dimension of a graph G with respect to a class A of graphs is the minimum k such that G is the intersection of some k graphs on the vertex set V (G) belonging to A. In this paper we follow [ Kratochv́ıl J., Tuza Z.: Intersection dimensions of graph classes, Graphs and Combinatorics 10 (1994), 159– 168 ] and show that for some pairs of graph classes A, B the intersectio...