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Minimum clique cover in clawfree perfect graphs and the weak EdmondsJohnson property
"... We give new algorithms for the minimum (weighted) clique cover in a clawfree perfect graph G, improving the complexity from O(V (G)  5) to O(V (G)  3). The new algorithms build upon neat reformulations of the problem: it basically reduces either to solving a 2SAT instance (in the unweighted ..."
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We give new algorithms for the minimum (weighted) clique cover in a clawfree perfect graph G, improving the complexity from O(V (G)  5) to O(V (G)  3). The new algorithms build upon neat reformulations of the problem: it basically reduces either to solving a 2SAT instance (in the unweighted
ClawFree Graphs  a Survey.
, 1996
"... In this paper we summarize known results on clawfree graphs. The paper is subdivided into the following chapters and sections: 1. Introduction 2. Paths, cycles, hamiltonicity a) Preliminaries b) Degree and neighborhood conditions c) Local connectivity conditions d) Further forbidden subgraph ..."
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Cited by 12 (1 self)
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In this paper we summarize known results on clawfree graphs. The paper is subdivided into the following chapters and sections: 1. Introduction 2. Paths, cycles, hamiltonicity a) Preliminaries b) Degree and neighborhood conditions c) Local connectivity conditions d) Further forbidden
A Combinatorial Algorithm for the Minimum Weighted Coloring Problem on ClawFree Perfect Graphs
 INTERNATIONAL CONFERENCE ON GRAPH THEORY AND COMBINATORICS AND THE SECOND CROSSSTRAIT CONFERENCE ON GRAPH THEORY AND COMBINATORICS
, 2002
"... Given a graph G = (V,E) with a nonnegative integral weight w(v) on each vertex v, the minimum weighted coloring problem is to find stable sets S1, S2, · · · , St in V and nonnegative integers x(S1), x(S2), · · · , x(St) such that for each vertex v ∈ V the sum ∑v∈Si x(Si) ≥ w(v) and that ∑ti= ..."
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Cited by 5 (0 self)
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weighted coloring problem on clawfree perfect graphs. Let us introduce some notions. A claw is the complete bipartite graph K1,3; a graph is called clawfree if none of its induced subgraphs is a claw. Berge proposed to call a graph perfect if, for each of its induced subgraphs H, the chromatic number
Clawfree circularperfect graphs
 EUROCOMB07 EUROPEAN CONFERENCE ON COMBINATORICS, GRAPH THEORY AND APPLICATIONS, ESPAGNE
, 2007
"... The circular chromatic number of a graph is a wellstudied refinement of the chromatic number. Circularperfect graphs is a superclass of perfect graphs defined by means of this more general coloring concept. This paper studies clawfree circularperfect graphs. A consequence of the strong perfect g ..."
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Cited by 12 (2 self)
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The circular chromatic number of a graph is a wellstudied refinement of the chromatic number. Circularperfect graphs is a superclass of perfect graphs defined by means of this more general coloring concept. This paper studies clawfree circularperfect graphs. A consequence of the strong perfect
Factor Graphs and the SumProduct Algorithm
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1998
"... A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple c ..."
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Cited by 1787 (72 self)
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computational rule, the sumproduct algorithm operates in factor graphs to computeeither exactly or approximatelyvarious marginal functions by distributed messagepassing in the graph. A wide variety of algorithms developed in artificial intelligence, signal processing, and digital communications can
Reconfiguring independent sets in clawfree graphs
, 2014
"... Abstract. We present a polynomialtime algorithm that, given two independent sets in a clawfree graph G, decides whether one can be transformed into the other by a sequence of elementary steps. Each elementary step is to remove a vertex v from the current independent set S and to add a new vertex w ..."
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Cited by 8 (3 self)
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Abstract. We present a polynomialtime algorithm that, given two independent sets in a clawfree graph G, decides whether one can be transformed into the other by a sequence of elementary steps. Each elementary step is to remove a vertex v from the current independent set S and to add a new vertex
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices
A Threshold of ln n for Approximating Set Cover
 JOURNAL OF THE ACM
, 1998
"... Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NPhar ..."
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Cited by 778 (5 self)
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Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NP
Planning Algorithms
, 2004
"... This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning ..."
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Cited by 1108 (51 self)
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This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning
TRACEABILITY IN SMALL CLAWFREE GRAPHS
"... Abstract. We prove that a clawfree, 2connected graph with fewer than 18 vertices is traceable, and we determine all nontraceable, clawfree, 2connected graphs with exactly 18 vertices and a minimal number of edges. This complements a result of Matthews on Hamiltonian graphs. 1. ..."
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Abstract. We prove that a clawfree, 2connected graph with fewer than 18 vertices is traceable, and we determine all nontraceable, clawfree, 2connected graphs with exactly 18 vertices and a minimal number of edges. This complements a result of Matthews on Hamiltonian graphs. 1.
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