Constrained chords in strongly chordal and distance-hereditary graphs - McKee, Terry A. (Utilitas Mathematica, 2012)
The classes of chordal, strongly chordal, and distance-hereditary graphs can be characterized by sufficiently large cycles having specific kinds of chords. Those chords can be restricted to those that form triangles or quadrangles with edges of the cycles. Doing so motivates a new subclass of distance-hereditary graphs that has a variety of characterizations, including that their blocks are {P 4, 2K 2, K 3,3,K 2,2,2}-free.