---
tag: 8CBQ3NEPBM
kind: concept
name: Trapezoid graph
sources:
  - wikipedia: en:31675608@r1365289064
    locator: Trapezoid graph
    note: adopted
    mention: wikipedia://en/31675608
    sections: [Summary]
same_as:
  wikidata: Q7835582
  wikipedia: Trapezoid graph
inventory: [VFWC1EAED9]
---

## Summary

In graph theory, **trapezoid graphs** are intersection graphs of trapezoids between two horizontal lines. They are a class of co-comparability graphs that contain interval graphs and permutation graphs as subclasses. A graph is a **trapezoid graph** if there exists a set of trapezoids corresponding to the vertices of the graph such that two vertices are joined by an edge if and only if the corresponding trapezoids intersect. Trapezoid graphs were introduced by Dagan, Golumbic, and Pinter in 1988. There exists ${O}(n\log n)$ algorithms for chromatic number, weighted [[independent set|08ANQHHG3P]], clique cover, and maximum weighted clique.