In the
mathematical area of
graph theory, a
chordal graph is one in which all
cycles of four or more
vertices have a
chord, which is an
edge that is not part of the cycle but connects two vertices of the cycle. Equivalently, every
induced cycle in the graph should have at most three vertices. The chordal graphs may also be characterized as the graphs that have perfect elimination orderings, as the graphs in which each minimal separator is a clique, and as the
intersection graphs of subtrees of a tree. They are sometimes also called
rigid circuit graphs or
triangulated graphs.