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- W2366702955 abstract "This thesis studies an extension of both interval and permutation graphs known as II-graphs (Interval-Interval or trapezoidal graphs). Given two parallel horizontal lines with n intervals on each line, for any interval of the top line there is exactly one trapezoid joining it with an interval of the lower line. Each such trapezoid corresponds to a vertex of the II-graph, where two vertices are adjacent if and only if their corresponding trapezoids intersect. It is known that II-graphs exhibit many interesting properties such as being weakly chordal, co-comparability and asteroidal-triple free. Their complements are transitively orientable with an interval order of dimension two.This thesis presents an $O(nsp3$) algorithm for solving the II-graph recognition problem. Using an operation for splitting a vertex into two (called the Vertex Splitting Operation), our recognition algorithm will transform a given graph into a permutation graph with some special properties if and only if the given graph is an II-graph. Unlike other II-graph recognition algorithms, our algorithm will also construct an II-representation. We will also show that the Vertex Splitting Operation exhibits various interesting properties when applied to other families of graphs, including perfect graphs, chordal graphs and interval graphs." @default.
- W2366702955 created "2016-06-24" @default.
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- W2366702955 date "1990-01-01" @default.
- W2366702955 modified "2023-09-23" @default.
- W2366702955 title "A recognition algorithm for II-graphs" @default.
- W2366702955 hasPublicationYear "1990" @default.
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