Symmetric graph-theoretic roles of two-pairs and chords of cycles

Abstract

Although the notion of a two-pair (a pair of vertices between which all induced paths have length 2) was invented for the class of weakly chordal graphs, two-pairs can also play a fundamental role for smaller graph classes. Indeed, two-pairs and chords of cycles can collaborate symmetrically to give parallel characterizations of weakly chordal, chordal, and strongly chordal graphs (and of distance-hereditary graphs).