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The strong perfect graph theorem
 ANNALS OF MATHEMATICS
, 2006
"... A graph G is perfect if for every induced subgraph H, the chromatic number of H equals the size of the largest complete subgraph of H, and G is Berge if no induced subgraph of G is an odd cycle of length at least five or the complement of one. The “strong perfect graph conjecture” (Berge, 1961) asse ..."
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Cited by 285 (23 self)
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) asserts that a graph is perfect if and only if it is Berge. A stronger conjecture was made recently by Conforti, Cornuéjols and Vuˇsković — that every Berge graph either falls into one of a few basic classes, or admits one of a few kinds of separation (designed so that a minimum counterexample to Berge’s
A general approximation technique for constrained forest problems
 SIAM J. COMPUT.
, 1995
"... We present a general approximation technique for a large class of graph problems. Our technique mostly applies to problems of covering, at minimum cost, the vertices of a graph with trees, cycles, or paths satisfying certain requirements. In particular, many basic combinatorial optimization proble ..."
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Cited by 414 (21 self)
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We present a general approximation technique for a large class of graph problems. Our technique mostly applies to problems of covering, at minimum cost, the vertices of a graph with trees, cycles, or paths satisfying certain requirements. In particular, many basic combinatorial optimization
Cones of matrices and setfunctions and 01 optimization
 SIAM JOURNAL ON OPTIMIZATION
, 1991
"... It has been recognized recently that to represent a polyhedron as the projection of a higher dimensional, but simpler, polyhedron, is a powerful tool in polyhedral combinatorics. We develop a general method to construct higherdimensional polyhedra (or, in some cases, convex sets) whose projection a ..."
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Cited by 347 (7 self)
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of inequalities, such that already the first system includes clique, odd hole, odd antihole, wheel, and orthogonality constraints. In particular, for perfect (and many other) graphs, this first system gives the vertex packing polytope. For various classes of graphs, including tperfect graphs, it follows
Approximating the permanent
 SIAM J. Computing
, 1989
"... Abstract. A randomised approximation scheme for the permanent of a 01 matrix is presented. The task of estimating a permanent is reduced to that of almost uniformly generating perfect matchings in a graph; the latter is accomplished by simulating a Markov chain whose states are the matchings in the ..."
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Cited by 345 (26 self)
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Abstract. A randomised approximation scheme for the permanent of a 01 matrix is presented. The task of estimating a permanent is reduced to that of almost uniformly generating perfect matchings in a graph; the latter is accomplished by simulating a Markov chain whose states are the matchings
Cryptographic Limitations on Learning Boolean Formulae and Finite Automata
 PROCEEDINGS OF THE TWENTYFIRST ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING
, 1989
"... In this paper we prove the intractability of learning several classes of Boolean functions in the distributionfree model (also called the Probably Approximately Correct or PAC model) of learning from examples. These results are representation independent, in that they hold regardless of the syntact ..."
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Cited by 347 (14 self)
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algorithm is only required to obtain a slight advantage in prediction over random guessing. The techniques used demonstrate an interesting duality between learning and cryptography. We also apply our results to obtain strong intractability results for approximating a generalization of graph coloring.
SET COLORINGS IN PERFECT GRAPHS
, 2009
"... Abstract. For a nontrivial connected graph G, let c: V (G) → N be a vertex coloring of G where adjacent vertices may be colored the same. For a vertex v ∈ V (G), the neighborhood color set NC(v) is the set of colors of the neighbors of v. The coloring c is called a set coloring if NC(u) 6 = NC(v) fo ..."
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Abstract. For a nontrivial connected graph G, let c: V (G) → N be a vertex coloring of G where adjacent vertices may be colored the same. For a vertex v ∈ V (G), the neighborhood color set NC(v) is the set of colors of the neighbors of v. The coloring c is called a set coloring if NC(u) 6 = NC
Precoloring extension. III. Classes of perfect graphs
"... We continue the study of the following general problem on vertex colorings of graphs. Suppose that some vertices of a graph G are assigned to some colors. Can this “precoloring” be extended to a proper coloring of G with at most k colors (for some given k)? Here we investigate the complexity status ..."
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Cited by 38 (0 self)
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of precoloring extendibility on some classes of perfect graphs, giving good characterizations (necessary and sufficient conditions) that lead to algorithms with linear or polynomial running time. It is also shown how a larger subclass of perfect graphs can be derived from graphs containing no induced path
A class of perfectly contractile graphs
 Journal of Combinatorial Theory B
, 1997
"... Abstract. We consider the class A of graphs that contain no odd hole, no antihole, and no “prism ” (a graph consisting of two disjoint triangles with three disjoint paths between them). We prove that every graph G ∈ A different from a clique has an “even pair ” (two vertices that are not joined by a ..."
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Cited by 9 (6 self)
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that the contraction of this pair yields a graph in A. This entails a polynomialtime algorithm, based on successively contracting even pairs, to color optimally every graph in A. This generalizes several results concerning some classical families of perfect graphs. 1
Defective list colorings of planar graphs
 Bull. Inst. Combin. Appl
, 1999
"... We combine the concepts of list colorings of graphs with the concept of defective colorings of graphs and introduce the concept of defective list colorings. We apply these concepts to vertex colorings of various classes of planar graphs. A defective coloring with defect d is a coloring of the vertic ..."
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Cited by 25 (0 self)
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We combine the concepts of list colorings of graphs with the concept of defective colorings of graphs and introduce the concept of defective list colorings. We apply these concepts to vertex colorings of various classes of planar graphs. A defective coloring with defect d is a coloring
Perfectly Colourable Graphs
, 2011
"... We define a perfect coloring of a graph G as a proper coloring of G such that every connected induced subgraph H of G uses exactly ω(H) many colors where ω(H) is the clique number of H. A graph is perfectly colorable if it admits a perfect coloring. We show that the class of perfectly colorable gra ..."
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We define a perfect coloring of a graph G as a proper coloring of G such that every connected induced subgraph H of G uses exactly ω(H) many colors where ω(H) is the clique number of H. A graph is perfectly colorable if it admits a perfect coloring. We show that the class of perfectly colorable
Results 1  10
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