Independent separator graphs

Abstract

As almost a parody of chordal graphs, the class of graphs in which all minimal vertex separators - minimal sets of vertices whose removal increases the number of components - are independent is the same as the class of graphs in which no cycle has a unique chord. The subclass in which every cycle has an even number of chords also has an independent separator-type characterization in terms of sets o,f edges whose removal increases the number of components.