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Abstract: In this paper, we present a new relationship between concept lattices and graphs. Given a binary relation R, we define an underlying graph GR , and establish a one-to-one correspondence between the set of elements of the concept lattice of R and the set of minimal separators of GR . (Update)
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BibTeX entry: (Update)
A. Berry and A. Sigayret. Representing a concept lattice by a graph. Proceedings of Discrete Maths and Data Mining Workshop, 2nd SIAM Conference on Data Mining (SDM'02), Arlington (VA), April 2002, submitted to Discrete Applied Mathematics. http://citeseer.ist.psu.edu/article/berry02representing.html More
@inproceedings{ berry02representing,
author = "A. Berry and A. Sigayret",
title = "Representing a concept lattice by a graph",
booktitle = "Proceedings of Discrete Maths and Data Mining Workshop, 2nd
SIAM Conference on Data Mining (SDM'02), Arlington (VA)",
month = apr,
note = "submitted to Discrete Applied Mathematics.",
year = "2002",
url = "citeseer.ist.psu.edu/article/berry02representing.html" }
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178 Algorithmic aspects of vertex elimination on graphs (context) - Rose, Tarjan et al. - 1976
109 New Algorithms for Fast Discovery of Association Rules - Zaki, Parthasarathy et al. - 1997
90 On rigid circuit graphs (context) - Dirac - 1961
61 Decomposition by clique separators (context) - Tarjan - 1985
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23 Two basic algorithms in concept analysis (context) - Ganter - 1984
21 How to use the minimal separators of a graph for its chordal.. - Parra, Sche - 1995
17 A Fast Algorithm for building Lattices (context) - Nourine, Raynaud - 1999
17 Separability generalizes Dirac's theorem - Berry, Bordat - 1998
16 Optimal decomposition by clique separators (context) - Leimer - 1993
15 Generating all the minimal separators of a graph - Berry, Bordat et al. - 2000
14 Treewidth and pathwidth of cocomparability graphs of bounded.. (context) - Kloks, Kratsch et al. - 1993
12 Listing all minimal separators of a graph - Kloks, Kratsch - 1998
12 Structural and algorithmic aspects of chordal graph embeddin.. - Parra - 1996
10 Aspects algorithmiques des triangulations minimales des grap.. (context) - Todinca - 1999
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8 cient Algorithm for Minimal Triangulation (context) - Berry, Wide-Range - 1999
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6 A Framework for Incremental Generation of Frequent Closed It.. (context) - Valtchef, Missaoui et al. - 2002
5 Discrete Applied Mathematics (context) - Berry, Bordat et al. - 2001
5 Designing Class Hierarchies of Object Database Schemes (context) - Yahia, Lakhal et al. - 1997
4 Weak separation lattices of graphs (context) - Sabidussi - 1976
4 On Halin-Lattices in Graphs (context) - Hager - 1983
4 Dsarticulation d'un graphe (context) - Berry - 1998
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4 Triangulating graphs without asteroidal triples (context) - Mhring - 1996
3 Minimale Triangulationene AT-freier Graphen (context) - Meister - 2000
3 Knowledge Discovery through Iterative Transformation of Conc.. (context) - Pfaltz, Taylor - 2002
3 Orthotreillis et sparabilit dans un graphe non-orient (context) - Berry, Bordat - 1999
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3 Clique minimal separator decomposition (context) - Berry, Bordat - 1997
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