We prove that if $ p\ge n^{-\frac {1}{3}+\beta} $ for some $\beta> 0$, then asymptotically
almost surely the binomial random graph $ G (n, p) $ has a $ K_3 $-packing containing all …

We prove that the number of perfect matchings in 𝒢 (n, d) is asymptotically normal when nn
is even, d→∞ d → ∞ as n→∞ n → ∞, and d= O (n 1/7/log n) d= O\left (n^ 1/7/\log n\right) …

arXiv:2012.01492v3 [math.CO] 1 Feb 2023 Page 1 Triangles and subgraph probabilities in
random regular graphs Pu Gao ∗ University of Waterloo pu.gao@uwaterloo.ca Abstract We …

Given an $ n\times n $ symmetric matrix $ W\in [0, 1]^{[n]\times [n]} $, let ${\mathcal G}(n, W)
$ be the random graph obtained by independently including each edge $ jk\in\binom {[n]}{2} …

arXiv:2203.03006v1 [math.CO] 6 Mar 2022 Large cycles in generalized Johnson graphs Page
1 arXiv:2203.03006v1 [math.CO] 6 Mar 2022 Large cycles in generalized Johnson graphs …

Let be a uniformly random m-edge subgraph of the complete bipartite graph with bipartition,
where,. Given a real number such that and are integers, let be a random subgraph of with …