Random algebraic construction of extremal graphs
نویسندگان
چکیده
منابع مشابه
Random algebraic construction of extremal graphs
We present a motivated construction of large graphs not containing a given complete bipartite subgraph. The key insight is that the algebraic constructions yield very non-smooth probability distributions. MSC classes: 05C35, 05D99
متن کاملExtremal subgraphs of random graphs
We shall prove that if L is a 3-chromatic (so called "forbidden") graph, and -R" is a random graph on n vertices, whose edges are chosen indepen-6" is a bipartite subgraph of R" of maximum size, -F" is an L-free subgraph of R" of maximum size, dently, with probability p, and then (in some sense) F" and 6" are very near to each other: almost surely they have almost the same number of edges, and ...
متن کاملExtremal subgraphs of random graphs
Let K` denote the complete graph on ` vertices. We prove that there is a constant c = c(`), such that whenever p ≥ n−c, with probability tending to 1 when n goes to infinity, every maximum K`-free subgraph of the binomial random graph Gn,p is (`− 1)partite. This answers a question of Babai, Simonovits and Spencer [BSS90]. The proof is based on a tool of independent interest: we show, for instan...
متن کاملExtremal Results in Random Graphs
According to Paul Erdős [Some notes on Turán’s mathematical work, J. Approx. Theory 29 (1980), page 4] it was Paul Turán who “created the area of extremal problems in graph theory”. However, without a doubt, Paul Erdős popularized extremal combinatorics, by his many contributions to the field, his numerous questions and conjectures, and his influence on discrete mathematicians in Hungary and al...
متن کاملExtremal Cuts of Sparse Random Graphs
For Erdős-Rényi random graphs with average degree γ, and uniformly random γ-regular graph on n vertices, we prove that with high probability the size of both the Max-Cut and maximum bisection are n( γ 4 + P∗ √ γ 4 + o( √ γ)) + o(n) while the size of the minimum bisection is n( γ 4 − P∗ √ γ 4 + o( √ γ)) + o(n). Our derivation relates the free energy of the anti-ferromagnetic Ising model on such ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the London Mathematical Society
سال: 2015
ISSN: 0024-6093,1469-2120
DOI: 10.1112/blms/bdv062