An i-chord of a cycle C is a chord that forms a new cycle with a length-i subpath of C when i is at most half the length of C. Define a graph to be s-strongly chordal if, for every i ∈{2,…,s + 2}, every cycle long enough to have an i-chord always has an i-chord. The 0-strongly chordal and 1-strongly chordal graphs are, respectively, the chordal and strongly chordal graphs. Several characterizations of s-strongly chordal graphs are proved, along with details of the class of 2-strongly chordal graphs.
['Terry A. McKee']
Strengthening Strongly Chordal Graphs