Maintenance of transitive closures and transitive reductions of graphs

A graph G is said to be super-connected if any minimum cut of G isolates a vertex. In a previous work due to the second author of this note, super-connected graphs which are both vertex transitive and edge transitive are characterized. In this note, we ...

The complement of the transitive closure of the complement of a transitive relation is transitive. We prove this fact in three ways, analyze the underlying structure and consider various refinement's and applications.

A graph is said to be super-connected if every minimum vertex cut isolates a vertex. A graph is said to be hyper-connected if each minimum vertex cut creates exactly two components, one of which is an isolated vertex. It is proved that a connected ...