View source for Comparability graph

The undirected [[graph]] $(P,E)$ on a [[partially ordered set]] $(P,{\le})$ in which two points are adjacent if they are comparable; that is, $xy$ is an edge of the graph if and only if $x < y$ or $y < x$.  Comparability graphs are characterised by the property that in any odd length closed path $x_1,\ldots,x_{2n+1}$ with $n \ge 2$ (so all $x_i,x_{i+1}$ are adjacent) there exists at least one "chord" $x_i,x_{i+2}$ (subscripts being taken in cyclic order).

====References====
* Andreas Brandstädt, Van Bang Le; Jeremy P. Spinrad, "Graph classes: a survey". SIAM Monographs on Discrete Mathematics and Applications '''3'''. Society for Industrial and Applied Mathematics (1999) {{ISBN|978-0-898714-32-6}} {{ZBL|0919.05001}}

{{TEX|done}}