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3,569
Perfection Thickness of Graphs
"... We determine the order of growth of the worst-case number of perfect subgraphs needed to cover an n-vertex graph. ..."
Abstract
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Cited by 1 (1 self)
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We determine the order of growth of the worst-case number of perfect subgraphs needed to cover an n-vertex graph.
MSC: 05C30 Enumeration in graph theory; 05C69 Dominating sets, independent sets, cliques
"... independent sets in an n-vertex graph. We give a new and simple proof of this result. ..."
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independent sets in an n-vertex 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 ..."
Abstract
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Cited by 797 (39 self)
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the maximum clique size in an N-vertex graph to within a factor of N ɛ is NP-hard.
A new approach to the maximum flow problem
- JOURNAL OF THE ACM
, 1988
"... All previously known efficient maximum-flow algorithms work by finding augmenting paths, either one path at a time (as in the original Ford and Fulkerson algorithm) or all shortest-length augmenting paths at once (using the layered network approach of Dinic). An alternative method based on the pre ..."
Abstract
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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 n-vertex 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 random-fault-tolerant (RFT) graph for an n-vertex 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 random-fault-tolerant (RFT) graph for an n-vertex 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 n-vertex graphs require\Omega\Gamma n) depth. This implies an exponential gap between the depth of monotone and nonmonotone circuits. ..."
Abstract
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Cited by 82 (10 self)
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We prove that monotone circuits computing the perfect matching function on n-vertex graphs require\Omega\Gamma n) depth. This implies an exponential gap between the depth of monotone and nonmonotone circuits.
Pathwidth and Three-Dimensional Straight-Line Grid Drawings of Graphs
"... We prove that every n-vertex graph G with pathwidth pw(G) has a three-dimensional straight-line 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 n-vertex graph G with pathwidth pw(G) has a three-dimensional straight-line grid drawing with O(pw(G) n) volume. Thus for
On domination in 2-connected cubic graphs
"... In 1996, Reed proved that the domination number, γ(G), of every n-vertex graph G with minimum degree at least 3 is at most 3n/8 and conjectured that γ(H) ≤ ⌈n/3 ⌉ for every connected 3-regular (cubic) n-vertex 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 n-vertex graph G with minimum degree at least 3 is at most 3n/8 and conjectured that γ(H) ≤ ⌈n/3 ⌉ for every connected 3-regular (cubic) n-vertex 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 n-vertex 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 n-vertex 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
