Trapezoid graph

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, clique cover, and maximum weighted clique.

Figure 2: Trapezoid representation of graph G.

Notes

References

Golumbic, Martin Charles (1980). "Algorithmic Graph Theory and Perfect Graphs" (Document). Academic Press. ISBN 0-444-51530-5. {{cite document}}: Invalid |ref=harv (help); Unknown parameter |url= ignored (help) Second edition, Annals of Discrete Mathematics 57, Elsevier, 2004.