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241.
Michael Krivelevich Benny Sudakov Prasad Tetali 《Random Structures and Algorithms》2006,29(2):180-193
We study a model of random graphs, where a random instance is obtained by adding random edges to a large graph of a given density. The research on this model has been started by Bohman and colleagues (Random Struct Algor 3 ; Random Struct Algor 4 ). Here we obtain a sharp threshold for the appearance of a fixed subgraph and for certain Ramsey properties. We also consider a related model of random k‐SAT formulas, where an instance is obtained by adding random k‐clauses to a fixed formula with a given number of clauses, and derive tight bounds for the non‐satisfiability of the thus‐obtained random formula. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2006 相似文献
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A classical theorem of Ghouila‐Houri from 1960 asserts that every directed graph on n vertices with minimum out‐degree and in‐degree at least contains a directed Hamilton cycle. In this paper we extend this theorem to a random directed graph , that is, a directed graph in which every ordered pair (u, v) becomes an arc with probability p independently of all other pairs. Motivated by the study of resilience of properties of random graphs, we prove that if , then a.a.s. every subdigraph of with minimum out‐degree and in‐degree at least contains a directed Hamilton cycle. The constant 1/2 is asymptotically best possible. Our result also strengthens classical results about the existence of directed Hamilton cycles in random directed graphs. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 49, 345–362, 2016 相似文献
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We derive a sufficient condition for a sparse graph G on n vertices to contain a copy of a tree T of maximum degree at most d on (1 − ε)n vertices, in terms of the expansion properties of G. As a result we show that for fixed d ≥ 2 and 0 < ε < 1, there exists a constant c = c(d, ε) such that a random graph G(n, c/n) contains almost surely a copy of every tree T on (1 − ε)n vertices with maximum degree at most d. We also prove that if an (n, D, λ)-graph G (i.e., a D-regular graph on n vertices all of whose eigenvalues, except the first one, are at most λ in their absolute values) has large enough spectral gap D/λ as a function of d and ε, then G has a copy of every tree T as above.
Research supported in part by a USA-Israeli BSF grant, by NSF grant CCR-0324906, by a Wolfensohn fund and by the State of
New Jersey.
Research supported in part by USA-Israel BSF Grant 2002-133, and by grants 64/01 and 526/05 from the Israel Science Foundation.
Research supported in part by NSF CAREER award DMS-0546523, NSF grant DMS-0355497, USA-Israeli BSF grant, and by an Alfred
P. Sloan fellowship. 相似文献
247.
Benny Sudakov 《Combinatorica》2007,27(4):509-518
We show that every K
4-free graph G with n vertices can be made bipartite by deleting at most n
2/9 edges. Moreover, the only extremal graph which requires deletion of that many edges is a complete 3-partite graph with
parts of size n/3. This proves an old conjecture of P. Erdős.
Research supported in part by NSF CAREER award DMS-0546523, NSF grant DMS-0355497, USA-Israeli BSF grant, and by an Alfred
P. Sloan fellowship. 相似文献
248.
Hao Ju Bryan D. McCloskeyAlyson C. Sagle Yuan-Hsuan WuVictor A. Kusuma Benny D. Freeman 《Journal of membrane science》2008
Potential fouling reducing coating materials were synthesized via free-radical photopolymerization of aqueous solutions of poly(ethylene glycol) diacrylate (PEGDA). Crosslinked PEGDA (XLPEGDA) exhibited high water permeability and good fouling resistance to oil/water mixtures. Water permeability increased strongly with increasing the water content in the prepolymerization water mixture, going from 10 to 150 L μm/(m2 h bar) as prepolymerization water content increased from 60 to 80 wt.%. However, molecular weight cutoff decreased as water content increased. These materials were applied to polysulfone (PSF) UF membranes to form coatings on the surface of the PSF membranes. Oil/water crossflow filtration experiments showed that the coated PSF membranes had water flux values 400% higher than that of an uncoated PSF membrane after 24 h of operation, and the coated membranes had higher organic rejection than the uncoated membranes. 相似文献
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