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- Noga Alon, Eldar Fischer, Michael Krivelevich, Mario Szegedy
- FOCS
- 1999

Let P be a property of graphs. An-test for P is a randomized algorithm which, given the ability to make queries whether a desired pair of vertices of an input graph G with n vertices are adjacent or not, distinguishes, with high probability, between the case of G satisfying P and the case that it has to be modified by adding and removing more than n 2 edges… (More)

- Noga Alon, Michael Krivelevich, Benny Sudakov
- Random Struct. Algorithms
- 1998

We consider the following probabilistic model of a graph on n labeled vertices. Ž. First choose a random graph G n, 1r2 , and then choose randomly a subset Q of vertices of size k and force it to be a clique by joining every pair of vertices of Q by an edge. The problem is to give a polynomial time algorithm for finding this hidden clique almost surely for… (More)

- David Burshtein, Michael Krivelevich, Simon Litsyn, Gadi Miller
- IEEE Transactions on Information Theory
- 2002

New upper bounds on the rate of low-density parity-check (LDPC) codes as a function of the minimum distance of the code are derived. The bounds apply to regular LDPC codes, and sometimes also to right-regular LDPC codes. Their derivation is based on combinatorial arguments and linear programming. The new bounds improve upon the previous bounds due to… (More)

- Michael Krivelevich, Benny Sudakov
- Journal of Graph Theory
- 2003

In this article we study Hamilton cycles in sparse pseudo-random graphs. We prove that if the second largest absolute value of an eigenvalue of a d-regular graph G on n vertices satisfies —————————————————— ðlog log nÞ 2 1000 log n ðlog log log nÞ d and n is large enough, then G is Hamiltonian. We also show how our main result can be used to prove that for… (More)

- Noga Alon, Michael Krivelevich, Benny Sudakov
- Combinatorics, Probability & Computing
- 2003

For a graph H and an integer n, the Turán number ex(n, H) is the maximum possible number of edges in a simple graph on n vertices that contains no copy of H. H is r-degenerate if every one of its subgraphs contains a vertex of degree at most r. We prove that, for any fixed bipartite graph H in which all degrees in one colour class are at most r, ex(n, H)… (More)

- Noga Alon, Gregory Gutin, Michael Krivelevich
- J. Algorithms
- 2004

Let P be an optimization problem, and let A be an approximation algorithm for P. The domination ratio domr(A, n) is the maximum real q such that the solution x(I) obtained by A for any instance I of P of size n is not worse than at least a fraction q of the feasible solutions of I. We describe a deterministic, polynomial time algorithm with domination ratio… (More)

- Michael Krivelevich
- Combinatorica
- 1997

It is proven that for k ≥ 4 and n > k every k-color-critical graph on n vertices has at least k−1 2 + k−3 2(k 2 −2k−1) n edges, thus improving a result of Gallai from 1963.

- Michael Krivelevich, Benny Sudakov
- Combinatorics, Probability & Computing
- 2003

We prove that for all values of the edge probability p(n) the largest eigenvalue of a random graph G(n, p) satisfies almost surely: λ 1 (G) = (1 + o(1)) max{ √ ∆, np}, where ∆ is a maximal degree of G, and the o(1) term tends to zero as max{ √ ∆, np} tends to infinity.

- Michael Krivelevich
- Random Struct. Algorithms
- 1995

- Alan M. Frieze, Michael Krivelevich
- J. Comb. Theory, Ser. B
- 2005