A cycle (black) with two chords (green). As for this part, the graph is chordal. Note that both chords are necessary: if one is removed, the other green edge with three black edges would form a cycle of four edges with no chord.
I, the copyright holder of this work, hereby release it into the public domain. This applies worldwide.
In case this is not legally possible: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.