Construction of a family of graphs with a small induced proper subgraph with minimum degree 3 Original Research Article

We investigate the following question proposed by Erdős: Is there a constant c such that, for each n, if G is a graph with n vertices, image edges, and image, then G contains an induced proper subgraph H with at least cn vertices and image Previously we showed that there exists no such constant image by constructing a family of graphs whose induced proper subgraph with minimum degree 3 contains at most image vertices. In this paper we present a construction of a family of graphs whose largest induced proper subgraph with minimum degree 3 is image. Also a similar construction of a graph with image vertices and image edges is given.