Editing Chordal graph (section)

==Relation to other graph classes==

===Subclasses===
[[Interval graph]]s are the intersection graphs of subtrees of [[path graph]]s, a special case of trees. Therefore, they are a subfamily of chordal graphs.

[[Split graph]]s are graphs that are both chordal and the [[complement (graph theory)|complements]] of chordal graphs. {{harvtxt|Bender|Richmond|Wormald|1985}} showed that, in the limit as {{mvar|n}} goes to infinity, the fraction of {{mvar|n}}-vertex chordal graphs that are split approaches one.

[[Ptolemaic graph]]s are graphs that are both chordal and [[Distance-hereditary graph|distance hereditary]].
[[Quasi-threshold graph]]s are a subclass of Ptolemaic graphs that are both chordal and [[cograph]]s. [[Block graph]]s are another subclass of Ptolemaic graphs in which every two maximal cliques have at most one vertex in common. A special type is [[windmill graph]]s, where the common vertex is the same for every pair of cliques.

[[Strongly chordal graph]]s are graphs that are chordal and contain no {{mvar|n}}-sun (for {{math|''n'' ≥ 3}}) as an induced subgraph. Here an {{mvar|n}}-sun is an {{mvar|n}}-vertex chordal graph {{mvar|G}} together with a collection of {{mvar|n}} degree-two vertices, adjacent to the edges of a [[Hamiltonian cycle]] in&nbsp;{{mvar|G}}.

[[k-tree|{{mvar|K}}-trees]] are chordal graphs in which all maximal cliques and all maximal clique separators have the same size.<ref name="patil86">{{harvtxt|Patil|1986}}.</ref> [[Apollonian network]]s are chordal maximal [[planar graph]]s, or equivalently planar 3-trees.<ref name="patil86"/> Maximal [[outerplanar graph]]s are a subclass of 2-trees, and therefore are also chordal.

===Superclasses===
Chordal graphs are a subclass of the well known [[perfect graph]]s. 
Other superclasses of chordal graphs include weakly chordal graphs, [[cop-win graph]]s, odd-hole-free graphs, [[even-hole-free graph]]s, and [[Meyniel graph]]s. Chordal graphs are precisely the graphs that are both odd-hole-free and even-hole-free (see [[hole (graph theory)|holes]] in graph theory).

Every chordal graph is a [[strangulated graph]], a graph in which every [[peripheral cycle]] is a triangle, because peripheral cycles are a special case of induced cycles. Strangulated graphs are graphs that can be formed by [[clique-sum]]s of chordal graphs and maximal planar graphs. Therefore, strangulated graphs include [[maximal planar graph]]s.{{sfnp|Seymour|Weaver|1984}}