Trapezoid graphs and generalizations, geometry and algorithms

Trapezoid Graphs and Generalizations, Geometry and Algorithms

Trapezoid graphs are a class of cocomparability graphs containing interval graphs and permutation graphs as subclasses. They were introduced by Dagan et al. [3]. They propose an 0(n2) algorithm for chromatic number and a less efficient algorithm for maximum clique on trapezoid graphs. Based on a geometric representation of trapezoid graphs by boxes in the plane we design optimal, i.e., O(n log ...

Treelike and Chordal Graphs: Algorithms and Generalizations

Graph-Theoretic Algorithms Project Report Trapezoid Graphs

Trapezoid graphs are intersection graphs of trapezoids between two horizontal lines. They generalize both interval graphs and permutation graphs. Interval graphs are intersection graphs of intervals on the real line. Permutation graphs are intersection graphs of straight lines between two horizontal lines. They can be represented by a permutation diagram consisting of a pair of horizontal lines...

Tenacity and rupture degree parameters for trapezoid graphs

Reliability of networks is an important issue in the field of graph and network. Computation of network vulnerability parameters is NP-complete for popular network topologies such as tree, Mesh, Cube, etc.In this paper, we will show that the tenacity and rupture degree parameters for trapezoid graphs can be computed in polynomial time.

Circular and Circle Trapezoid Graphs

Along with the direction that generalizes interval graphs and permutation graphs to trapezoid graphs, researchers are now trying to generalize the class known as trapezoid graphs. A circle trapezoid is the region in a circle that lies between two non-crossing chords; thus, circle trapezoid graphs are the intersecting graphs of circle trapezoids within a circle. It should be noted that circle tr...