Subclasses of Normal Helly Circular-Arc Graphs

A Helly circular-arc model M = (C,A) is a circle C together with a Helly family \A of arcs of C. If no arc is contained in any other, then M is a proper Helly circular-arc model, if every arc has the same length, then M is a unit Helly circular-arc model, and if there are no two arcs covering the circle, then M is a normal Helly circular-arc model. A Helly (resp. proper Helly, unit Helly, normal Helly) circular-arc graph is the intersection graph of the arcs of a Helly (resp. proper Helly, unit Helly, normal Helly) circular-arc model. In this article we study these subclasses of Helly circular-arc graphs. We show natural generalizations of several properties of (proper) interval graphs that hold for some of these Helly circular-arc subclasses. Next, we describe characterizations for the subclasses of Helly circular-arc graphs, including forbidden induced subgraphs characterizations. These characterizations lead to efficient algorithms for recognizing graphs within these classes. Finally, we show how do these classes of graphs relate with straight and round digraphs.Comment: 39 pages, 13 figures. A previous version of the paper (entitled Proper Helly Circular-Arc Graphs) appeared at WG'0

Consecutive Retrieval Property - Revisited

: The connection between the consecutive retrieval property and interval graphs is explored. Necessary and sufficient conditions for the existence of the consecutive retrieval property are developed from the standpoint of graph theory. These conditions are based on a characterization of unit interval graphs developed in this paper. Keywords: Consecutive Retrieval Property, Unit Interval Graphs, Information Retrieval. 1 Introduction In 1972, Ghosh [6, 7] introduced the concept of the consecutive retrieval file organization. Easwaran [3, 4] developed a graph theoretic approach for analyzing the consecutive retrieval property and established some necessary conditions for its existence. Our main objectives are to clarify some of the myths regarding the relationship between the consecutive retrieval property and interval graphs and to develop necessary and sufficient conditions for the existence of the consecutive retrieval property from the standpoint of graph theory. A storage media in ..