Circular and Circle Trapezoid Graphs
نویسنده
چکیده
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 trapezoid graphs properly contain trapezoid graphs, circle graphs and circular-arc graphs as subclasses. Circle trapezoid graphs should not be confused with circular trapezoid graphs. A circular trapezoid is the region within two parallel circles that lies between two non-crossing segments; circular trapezoid graphs are the intersecting graphs of circular trapezoids between two
منابع مشابه
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 ...
متن کامل2 Trapezoid Graphs
Trapezoid graphs are a class of cocomparability graphs containing interval graphs and permutation graphs as subclasses. They were introduced by Dagan, Golumbic and Pinter DGP]. They propose an O(n 2) algorithm for chromatic number and a less eecient algorithm for maximum clique on trapezoid graphs. Based on a geometric representation of trapezoid graphs by boxes in the plane we design optimal, ...
متن کاملMinimum Weight Feedback Vertex Sets in Circle n-Gon Graphs and Circle Trapezoid Graphs
A circle n-gon is the region between n non-crossing chords of a circle; the sides of a circle n-gon are either chords or arcs of the circle. A circle n-gon graph is the intersection graph of a family of circle n-gons in a circle. The family of circle trapezoid graphs is exactly the family of circle 2-gon graphs and the family of circle graphs is exactly the family of circle 1-gon graphs. The fa...
متن کاملIntersection Graphs: An Introduction
Intersection graphs are very important in both theoretical as well as application point of view. Depending on the geometrical representation, different type of intersection graphs are defined. Among them interval, circular-arc, permutation, trapezoid, chordal, disk, circle graphs are more important. In this article, a brief introduction of each of these intersection graphs is given. Some basic ...
متن کاملOn graph classes with logarithmic boolean-width
Boolean-width is a recently introduced graph parameter. Many problems are fixed parameter tractable when parametrized by boolean-width, for instance "Minimum Weighted Dominating Set" (MWDS) problem can be solved in O∗(23k) time given a boolean-decomposition of width k, hence for all graph classes where a boolean-decomposition of width O(log n) can be found in polynomial time, MWDS can be solved...
متن کامل