Advances in MathematicsD. Conlon, J. Fox, and Y. Zhao, Extremal results in sparse pseudorandom graphs, arXiv:1204.6645.D. Conlon, J. Fox and Y. Zhao, Extremal results in sparse pseudorandom graphs, Adv. Math. 256 (2014), 206-290....
Extremal results for random discrete structures 2016, Annals of Mathematics Hypergraph containers 2015, Inventiones Mathematicae Independent sets in hypergraphs 2015, Journal of the American Mathematical Society Dirac's theorem for random graphs 2012, Random Structures and Algorithms On Κ4-free subgraphs ...
In this survey we consider extremal problems for cycles of prescribed lengths in graphs. The general extremal problem is cast as follows: if...
B. Bollobás: Random Graphs, Academic Press, (1985). Second edition. Cambridge Studies in Advanced Mathematics, 73. Cambridge University Press, Cambridge, 2001. xviii+498 pp. Google Scholar B. Bollobás: Extremal graph theory with emphasis on probabilistic methods, Conference Board of Mathematical...
The next proposition introduces results from [25,28,37]. For the sake of completeness, we provide a proof in Appendix A. Proposition 1. LetΩ be a finite and non-empty set, and let { X ω } ω ∈ Ω be a collection of discrete random variables. Then, the following holds: (a) ...
Attempts to f i nd more accurate bounds for variousbipartite H, particularly complete bipartite graphs and even cycles, occupy a central place inextremal combinatorics. We refer the interested reader to [20] for a thorough and detailed survey.One of the few general results in this area, f i...
Some probabilistic and extremal results on subdivisions and odd subdivisions of graphsA probabilistic result of Bollob谩s and Catlin concerning the largest integer p so that a subdivision of Kp is contained in a random graph is generalized to a result concerning the largest integer p so that a ...
Turán’s extremal problem in random graphs: forbidding even cycles - Haxell, Kohayakawa, et al. - 1995 () Citation Context ...ct various results to be used later in the proofs of the theorems. 2.1. Resilience. The local resilience of random graphs with respect to being Hamiltonian [20]...
Using a result of Bukh and Conlon on Turán numbers, we prove that any rational number in [3/4,1]$$ \\left[3/4,1ight] $$ is optimal as an exponent for some finite family of forbidden subgraphs. Our upper bounds come equipped with randomized linear‐time algorithms that construct feed...
Next, we use the Differential Equations method to investigate a Ramsey-type threshold in random graphs. We conclude by studying a more complicated random graph process which has attracted recent attention, known as the Achlioptas process. Via the Layered Induction method, we determine precise ...