scholarly journals Linear-Time Recognition of Probe Interval Graphs

2015 ◽  
Vol 29 (4) ◽  
pp. 2006-2046 ◽  
Author(s):  
Ross M. McConnell ◽  
Yahav Nussbaum
Keyword(s):  
Linear Time ◽  
Interval Graphs ◽  
Probe Interval Graphs

scholarly journals Linear Time Recognition Algorithms and Structure Theorems for Bipartite Tolerance Graphs and Bipartite Probe Interval Graphs

2010 ◽  
Vol Vol. 12 no. 5 (Graph and Algorithms) ◽  
Author(s):  
David E. Brown ◽  
Arthur H. Busch ◽  
Garth Isaak
Keyword(s):  
Real Line ◽  
Positive Real Number ◽  
Linear Time ◽  
Interval Graph ◽  
Interval Graphs ◽  
Positive Real ◽  
Recognition Algorithms ◽  
Probe Interval Graphs ◽  
Tolerance Graphs ◽  
International Audience

Graphs and Algorithms International audience A graph is a probe interval graph if its vertices can be partitioned into probes and nonprobes with an interval associated to each vertex so that vertices are adjacent if and only if their corresponding intervals intersect and at least one of them is a probe. A graph G = (V, E) is a tolerance graph if each vertex v is an element of V can be associated to an interval I(v) of the real line and a positive real number t(v) such that uv is an element of E if and only if vertical bar I(u) boolean AND I(v)vertical bar >= min \t(u), t(v)\. In this paper we present O(vertical bar V vertical bar + vertical bar E vertical bar) recognition algorithms for both bipartite probe interval graphs and bipartite tolerance graphs. We also give a new structural characterization for each class which follows from the algorithms.

Simple linear time recognition of unit interval graphs

1995 ◽  
Vol 55 (2) ◽  
pp. 99-104 ◽  
Author(s):  
Derek G Corneil ◽  
Hiryoung Kim ◽  
Sridhar Natarajan ◽  
Stephan Olariu ◽  
Alan P Sprague
Keyword(s):  
Linear Time ◽  
Unit Interval ◽  
Interval Graphs

scholarly journals A characterization of cycle-free unit probe interval graphs

2009 ◽  
Vol 157 (4) ◽  
pp. 762-767 ◽  
Author(s):  
David E. Brown ◽  
J. Richard Lundgren ◽  
Li Sheng
Keyword(s):  
Interval Graphs ◽  
Probe Interval Graphs

scholarly journals A characterization of 2-tree probe interval graphs

2014 ◽  
Vol 34 (3) ◽  
pp. 509
Author(s):  
David E. Brown ◽  
Breeann M. Flesch ◽  
J. Richard Lundgren
Keyword(s):  
Interval Graphs ◽  
Probe Interval Graphs

scholarly journals Linear-Time Algorithms for Scattering Number and Hamilton-Connectivity of Interval Graphs

2013 ◽  
pp. 127-138
Author(s):  
Hajo Broersma ◽  
Jiří Fiala ◽  
Petr A. Golovach ◽  
Tomáš Kaiser ◽  
Daniël Paulusma ◽  
...  
Keyword(s):  
Linear Time ◽  
Interval Graphs ◽  
Linear Time Algorithms
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