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Modular Decomposition and Transitive Orientation
, 1999
"... A module of an undirected graph is a set X of nodes such for each node x not in X, either every member of X is adjacent to x, or no member of X is adjacent to x. There is a canonical linearspace representation for the modules of a graph, called the modular decomposition. Closely related to modular ..."
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Cited by 90 (14 self)
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A module of an undirected graph is a set X of nodes such for each node x not in X, either every member of X is adjacent to x, or no member of X is adjacent to x. There is a canonical linearspace representation for the modules of a graph, called the modular decomposition. Closely related to modular decomposition is the transitive orientation problem, which is the problem of assigning a direction to each edge of a graph so that the resulting digraph is transitive. A graph is a comparability graph if such an assignment is possible. We give O(n +m) algorithms for modular decomposition and transitive orientation, where n and m are the number of vertices and edges of the graph. This gives linear time bounds for recognizing permutation graphs, maximum clique and minimum vertex coloring on comparability graphs, and other combinatorial problems on comparability graphs and their complements.
Preformulation studies in
 Theory and Practice of Industrial Pharmacy Varghese Publishing Company
, 1986
"... of a microcanonical algorithm on the ±J spin glass model in d = 3. ..."
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Cited by 4 (0 self)
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of a microcanonical algorithm on the ±J spin glass model in d = 3.
A Graph Parsing Algorithm and Implementation
, 1993
"... This paper presents an algorithm for decomposing directed acyclic graphs (DAGs) into a heirarchy of subgraphs we call clans. The resulting parse tree is being used to partition and schedule program dependence graphs for efficient concurrent execution on a parallel system. The clans can be identified ..."
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Cited by 2 (2 self)
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This paper presents an algorithm for decomposing directed acyclic graphs (DAGs) into a heirarchy of subgraphs we call clans. The resulting parse tree is being used to partition and schedule program dependence graphs for efficient concurrent execution on a parallel system. The clans can be identified as able or unable to support parallel execution, and their connections with other clans is completely characterized in the parse tree. . 2 Definitions and Concepts
Convex CircuitFree coloration of an oriented graph
 REVISION FOR THE EUROPEAN JOURNAL OF COMBINATORICS
"... We introduce the convex circuitfree coloration and convex circuitfree chromatic number χa ( − → G) of an oriented graph − → G and establish various basic results. We show that the problem of deciding if an oriented graph verifies χa ( − → G) ≤ k is NPcomplete if k ≥ 3 and polynomial if k ≤ 2. We ..."
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We introduce the convex circuitfree coloration and convex circuitfree chromatic number χa ( − → G) of an oriented graph − → G and establish various basic results. We show that the problem of deciding if an oriented graph verifies χa ( − → G) ≤ k is NPcomplete if k ≥ 3 and polynomial if k ≤ 2. We exhibit an algorithm which finds the optimal convex circuitfree coloration for tournaments, and characterize the tournaments that are vertexcritical for the convex circuitfree coloration.
Relations In
"... We prove that any indecomposable (or prime) in nite relation strictly embeds an indecomposable relation which have same cardinal. ..."
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We prove that any indecomposable (or prime) in nite relation strictly embeds an indecomposable relation which have same cardinal.
INDECOMPOSABLE BINARY STRUCTURES
, 2009
"... The notion of interval is wellknown for linear orders. The analogue for (undirected) graphs is called module [25] or homogeneous set [6]. One uses also autonomous set [16, 21, 22] for partially ordered sets. It is still called interval for relations and multirelations [14, 15], and for directed gra ..."
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The notion of interval is wellknown for linear orders. The analogue for (undirected) graphs is called module [25] or homogeneous set [6]. One uses also autonomous set [16, 21, 22] for partially ordered sets. It is still called interval for relations and multirelations [14, 15], and for directed graphs [18, 24]. For 2structures [11, 13], it is called clan. In our framework, it is easier and more efficient to consider labelled 2structures [13], simply called binary structures [19]. Given a binary structure, a quotient is naturally associated with a partition in clans of its vertex set. The notions above were mainly introduced to obtain a simple notion of quotient. A binary structure admitting a nontrivial quotient is decomposable, otherwise it is indecomposable (or prime or primitive).