Requiring chords in cycles

Jamison proved that every cycle of length greater than three in a graph has a chord—in other words, the graph is chordal—if and only if every image-cycle is the sum of image triangles. This result generalizes to having or not having crossing chords and to having strong chords, with similar characterizations of a variety of graph classes that includes chordal bipartite, distance-hereditary, and strongly chordal graphs.