A Simpler Linear-Time Recognition of Circular-Arc Graphs

Characterizations and Linear Time Recognition of Helly Circular-Arc Graphs

A circular-arc model (C,A) is a circle C together with a collection A of arcs of C. If A satisfies the Helly Property then (C,A) is a Helly circular-arc model. A (Helly) circular-arc graph is the intersection graph of a (Helly) circular-arc model. Circular-arc graphs and their subclasses have been the object of a great deal of attention, in the literature. Linear time recognition algorithm have...

Linear-Time Recognition of Circular-Arc Graphs1

A graph G is a circular-arc graph if it is the intersection graph of a set of arcs on a circle. That is, there is one arc for each vertex of G, and two vertices are adjacent in G if and only if the corresponding arcs intersect. We give a linear-time algorithm for recognizing this class of graphs. When G is a member of the class, the algorithm gives a certificate in the form of a set of arcs tha...

Polynomial time recognition of unit circular-arc graphs

We present an efficient algorithm for recognizing unit circular-arc (UCA) graphs, based on a characterization theorem for UCA graphs proved by Tucker in the seventies. Given a proper circular-arc (PCA) graph G, the algorithm starts from a PCA model for G, removes all its circle-covering pairs of arcs and determines whether G is a UCA graph. We also give an O(N) time bound for Tucker’s 3/2-appro...

Induced Disjoint Paths in Circular-Arc Graphs in Linear Time

The Induced Disjoint Paths problem is to test whether an graph G on n vertices with k distinct pairs of vertices (si, ti) contains paths P1, . . . , Pk such that Pi connects si and ti for i = 1, . . . , k, and Pi and Pj have neither common vertices nor adjacent vertices (except perhaps their ends) for 1 ≤ i < j ≤ k. We present a linear-time algorithm that solves Induced Disjoint Paths and finds...

Linear-Time Recognition of Circular-Arc Graphs ; CU-CS-914-01