Optimal decomposition by clique separators
Discrete Mathematics
Triangulating graphs without asteroidal triples
Discrete Applied Mathematics
Efficient enumeration of all minimal separators in a graph
Theoretical Computer Science
Listing all Minimal Separators of a Graph
SIAM Journal on Computing
Separability generalizes Dirac's theorem
Discrete Applied Mathematics
A wide-range efficient algorithm for minimal triangulation
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
A fast algorithm for building lattices
Information Processing Letters
Asteroidal triples of moplexes
Discrete Applied Mathematics
Maintaining Class Membership Information
OOIS '02 Proceedings of the Workshops on Advances in Object-Oriented Information Systems
How to Use the Minimal Separators of a Graph for its Chordal Triangulation
ICALP '95 Proceedings of the 22nd International Colloquium on Automata, Languages and Programming
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Hi-index | 0.04 |
Concept lattices (also called Galois lattices) are an ordering of the maximal rectangles defined by a binary relation. In this paper, we present a new relationship between lattices and graphs: given a binary relation R, we define an underlying graph G"R, 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 G"R. We explain how to use the properties of minimal separators to define a sublattice, decompose a binary relation, and generate the elements of the lattice.