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Perfection Thickness of Graphs
"... We determine the order of growth of the worstcase number of perfect subgraphs needed to cover an nvertex graph. ..."
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Cited by 1 (1 self)
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We determine the order of growth of the worstcase number of perfect subgraphs needed to cover an nvertex graph.
MSC: 05C30 Enumeration in graph theory; 05C69 Dominating sets, independent sets, cliques
"... independent sets in an nvertex graph. We give a new and simple proof of this result. ..."
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independent sets in an nvertex graph. We give a new and simple proof of this result.
Proof verification and hardness of approximation problems
 IN PROC. 33RD ANN. IEEE SYMP. ON FOUND. OF COMP. SCI
, 1992
"... We show that every language in NP has a probablistic verifier that checks membership proofs for it using logarithmic number of random bits and by examining a constant number of bits in the proof. If a string is in the language, then there exists a proof such that the verifier accepts with probabilit ..."
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Cited by 797 (39 self)
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the maximum clique size in an Nvertex graph to within a factor of N ɛ is NPhard.
A new approach to the maximum flow problem
 JOURNAL OF THE ACM
, 1988
"... All previously known efficient maximumflow algorithms work by finding augmenting paths, either one path at a time (as in the original Ford and Fulkerson algorithm) or all shortestlength augmenting paths at once (using the layered network approach of Dinic). An alternative method based on the pre ..."
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Cited by 672 (33 self)
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to be shortest paths. The algorithm and its analysis are simple and intuitive, yet the algorithm runs as fast as any other known method on dense. graphs, achieving an O(n³) time bound on an nvertex graph. By incorporating the dynamic tree data structure of Sleator and Tarjan, we obtain a version
A Note on Sparse Networks Tolerating Random Faults for Cycles
"... An O(n)vertex graph G (n; p) is called a randomfaulttolerant (RFT) graph for an nvertex graph Gn if G (n; p) contains Gn as a subgraph with probability Prob(Gn,G ..."
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An O(n)vertex graph G (n; p) is called a randomfaulttolerant (RFT) graph for an nvertex graph Gn if G (n; p) contains Gn as a subgraph with probability Prob(Gn,G
Monotone Circuits for Matching Require Linear Depth
"... We prove that monotone circuits computing the perfect matching function on nvertex graphs require\Omega\Gamma n) depth. This implies an exponential gap between the depth of monotone and nonmonotone circuits. ..."
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Cited by 82 (10 self)
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We prove that monotone circuits computing the perfect matching function on nvertex graphs require\Omega\Gamma n) depth. This implies an exponential gap between the depth of monotone and nonmonotone circuits.
Pathwidth and ThreeDimensional StraightLine Grid Drawings of Graphs
"... We prove that every nvertex graph G with pathwidth pw(G) has a threedimensional straightline grid drawing with O(pw(G) n) volume. Thus for ..."
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Cited by 23 (12 self)
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We prove that every nvertex graph G with pathwidth pw(G) has a threedimensional straightline grid drawing with O(pw(G) n) volume. Thus for
On domination in 2connected cubic graphs
"... In 1996, Reed proved that the domination number, γ(G), of every nvertex graph G with minimum degree at least 3 is at most 3n/8 and conjectured that γ(H) ≤ ⌈n/3 ⌉ for every connected 3regular (cubic) nvertex graph H. In [1] this conjecture was disproved by presenting a connected cubic graph G on 6 ..."
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In 1996, Reed proved that the domination number, γ(G), of every nvertex graph G with minimum degree at least 3 is at most 3n/8 and conjectured that γ(H) ≤ ⌈n/3 ⌉ for every connected 3regular (cubic) nvertex graph H. In [1] this conjecture was disproved by presenting a connected cubic graph G
A Separator Theorem for Planar Graphs
, 1977
"... Let G be any nvertex planar graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than 2& & vertices. We exhibit an algorithm which ..."
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Cited by 461 (1 self)
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Let G be any nvertex planar graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than 2& & vertices. We exhibit an algorithm which
Results 1  10
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3,569