On 2-e. c. line-critical graphs (Q2747185)

For a fixed integer \(n\geq 1\), a graph is called \(n\)-existentially closed or \(n\)-e.c. if for every \(n\)-element subset \(S\) of the vertices, and for every subset \(T\) of \(S\), there is a vertex not in \(S\) which is joined to every vertex in \(T\) and to no vertex in \(S\setminus T\). The paper investigates the \(n\)-e.c. line-critical graphs. It classifies the 1-e.c. line-critical graphs and gives examples of 2-e.c. line critical graphs for all orders \(\geq 9\).