scholarly journals Recognizing edge clique graphs among interval graphs and probe interval graphs

2007 ◽  
Vol 20 (9) ◽  
pp. 1000-1004 ◽  
Author(s):  
Jing Kong ◽  
Yaokun Wu
Keyword(s):  
Interval Graphs ◽  
Probe Interval Graphs ◽  
Clique 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 Tree Spanners for Bipartite Graphs and Probe Interval Graphs

Algorithmica ◽  
2006 ◽  
Vol 47 (1) ◽  
pp. 27-51 ◽  
Author(s):  
Andreas Brandstadt ◽  
Feodor F. Dragan ◽  
Hoang-Oanh Le ◽  
Van Bang Le ◽  
Ryuhei Uehara
Keyword(s):  
Bipartite Graphs ◽  
Interval Graphs ◽  
Probe Interval Graphs

scholarly journals On probe interval graphs

1998 ◽  
Vol 88 (1-3) ◽  
pp. 315-324 ◽  
Author(s):  
F.R. McMorris ◽  
Chi Wang ◽  
Peisen Zhang
Keyword(s):  
Interval Graphs ◽  
Probe Interval Graphs

scholarly journals 2-Tree probe interval graphs have a large obstruction set

2005 ◽  
Vol 150 (1-3) ◽  
pp. 216-231 ◽  
Author(s):  
Nataša Pržulj ◽  
Derek G. Corneil
Keyword(s):  
Interval Graphs ◽  
Probe Interval Graphs

scholarly journals Tree Spanners for Bipartite Graphs and Probe Interval Graphs

2003 ◽  
pp. 106-118 ◽  
Author(s):  
Andreas Brandstädt ◽  
Feodor F. Dragan ◽  
Hoang-Oanh Le ◽  
Van Bang Le ◽  
Ryuhei Uehara
Keyword(s):  
Bipartite Graphs ◽  
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.

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