A chordal graph is a simple graph in which every graph cycle of length four and greater has a cycle
chord. In other words, a chordal graph is a graph possessing no chordless
cycles of length four or greater (cf. West 2000, p. 225; Gross and Yellen
2006, p. 437).

The numbers of simple chordal graphs on , 2, ... nodes are 1, 2, 4, 10, 27, 94, 393, ... (OEIS A048193). The first few are illustrated above,
though many are trivially chordal since they possess no cycles of length .

The corresponding numbers of simple connected chordal graphs are 1, 1, 2, 5, 15, 58, 272, ... (OEIS A048192). The first few
are illustrated above, though many are again chordal only trivially.

It is possible to recognize chordal graphs in linear time. Furthermore, a maximum clique of a chordal graph can be found in polynomial
time although the problem is NP-complete
for general graphs.

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