Interval graphs, circular-arc And circular-arc overlaps graphs

Circular-arc graphs are a new class of intersection graphs, defined for a set of arcs on a circle. A graph is a circular-arc graph, if it is the intersection graph of a finite set of arcs on a circle.That is, there exists one arc for each vertex of G and two vertices in G are adjacent in G,if and only if the corresponding arcs intersect.A vertex is said to dominate another vertex if there is an edge between the two vertices.If we bend the arc into a line, then the family of arcs is transformed into a family of intervals.Therefore, every interval graph is a CAG, where the opposite is always not true. However,these days CAG as well as interval graphs are being patronized very much. The combinatorial structures in CAG are varied and extensive, where it finds an application in many other fields such as biology, genetics, traffic control,computer science and particularly useful in cyclic scheduling and computer storage allocation problems etc.Circular-arc overlap graphs are a new class of overlap graphs introduced by Kashiwabara and Masuda [2], defined for a set of arcs on a circle.