Paper Info
Title
Subclasses of Normal Helly Circular-Arc Graphs
Abstract
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 these classes of graphs relate with straight and round digraphs.
Year
DOI
Venue
2011
10.1016/j.dam.2012.11.005
Discrete Applied Mathematics
Keywords
Field
DocType
Helly circular-arc graphs,Proper circular-arc graphs,Unit circular-arc graphs,Normal circular-arc graphs
Discrete mathematics,Graph,Combinatorics,Arc (geometry),Helly family,Helly's theorem,Generalization,Intersection graph,Mathematics
Journal
Volume
Issue
ISSN
161
7
0166-218X
Citations 
PageRank 
References 
5
0.42
0
Authors
3
Name
Order
Citations
PageRank
Min Chih Lin125921.22
Francisco J. Soulignac210110.56
Jayme Luiz Szwarcfiter361895.79