scholarly journals Lex-BFS and partition refinement, with applications to transitive orientation, interval graph recognition and consecutive ones testing

2000 ◽  
Vol 234 (1-2) ◽  
pp. 59-84 ◽  
Author(s):  
Michel Habib ◽  
Ross McConnell ◽  
Christophe Paul ◽  
Laurent Viennot
Keyword(s):  
Interval Graph ◽  
Graph Recognition ◽  
Transitive Orientation ◽  
Partition Refinement

A linear-time algorithm for proper interval graph recognition

1995 ◽  
Vol 56 (3) ◽  
pp. 179-184 ◽  
Author(s):  
Celina M.Herrera de Figueiredo ◽  
João Meidanis ◽  
Célia Picinin de Mello
Keyword(s):  
Linear Time ◽  
Time Algorithm ◽  
Interval Graph ◽  
Linear Time Algorithm ◽  
Graph Recognition ◽  
Proper Interval Graph

scholarly journals Closed graphs are proper interval graphs

2014 ◽  
Vol 22 (3) ◽  
pp. 37-44
Author(s):  
Marilena Crupi ◽  
Giancarlo Rinaldo
Keyword(s):  
Linear Time ◽  
Interval Graph ◽  
Simple Graph ◽  
Interval Graphs ◽  
Closed Graph ◽  
Graph Recognition ◽  
Proper Interval Graph ◽  
Linear Time Algorithms

Abstract Let G be a connected simple graph. We prove that G is a closed graph if and only if G is a proper interval graph. As a consequence we obtain that there exist linear-time algorithms for closed graph recognition.

scholarly journals A four-sweep LBFS recognition algorithm for interval graphs

2014 ◽  
Vol Vol. 16 no. 3 (Graph Theory) ◽  
Author(s):  
Peng Li ◽  
Yaokun Wu
Keyword(s):  
Linear Time ◽  
Interval Graph ◽  
Recognition Algorithm ◽  
Structure Theory ◽  
Time Interval ◽  
Breadth First Search ◽  
Input Graph ◽  
Graph Recognition ◽  
Unit Interval Graph ◽  
International Audience

Graph Theory International audience In their 2009 paper, Corneil et al. design a linear time interval graph recognition algorithm based on six sweeps of Lexicographic Breadth-First Search (LBFS) and prove its correctness. They believe that their corresponding 5-sweep LBFS interval graph recognition algorithm is also correct. Thanks to the LBFS structure theory established mainly by Corneil et al., we are able to present a 4-sweep LBFS algorithm which determines whether or not the input graph is a unit interval graph or an interval graph. Like the algorithm of Corneil et al., our algorithm does not involve any complicated data structure and can be executed in linear time.

scholarly journals Interval graph representation with given interval and intersection lengths

2015 ◽  
Vol 34 ◽  
pp. 108-117 ◽  
Author(s):  
Johannes Köbler ◽  
Sebastian Kuhnert ◽  
Osamu Watanabe
Keyword(s):  
Interval Graph ◽  
Graph Representation
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