A note on some kinds of hereditary bound graphs - Era, Hiroshi; Ogawa, Kenjiro; Tsuchiya, Morimasa (Utilitas Mathematica, 2008)
In this paper, we consider some properties of double bound graphs, upper bound graphs and semi bound graphs. A graph is a hereditary double bound graph if every induced subgraph is a double bound graph. We obtain a characterization of hereditary double bound graphs in terms of forbidden subgraphs. That is, a double bound graph is a hereditary double bound graph if and only if a 3-fan is not its induced subgraph. Similarly we obtain characterizations of hereditary upper bound graphs and hereditary semi bound graphs in terms of forbidden subgraphs.