Dingjia Mao
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View article: Hamilton cycles in regular graphs perturbed by a random 2-factor
Hamilton cycles in regular graphs perturbed by a random 2-factor Open
In this paper, we prove that for each $d \geq 2$, the union of a $d$-regular graph with a uniformly random $2$-factor on the same vertex set is Hamiltonian with high probability. This resolves a conjecture by Draganić and Keevash for all v…
View article: Hamiltonicity of sparse pseudorandom graphs
Hamiltonicity of sparse pseudorandom graphs Open
We show that every $(n,d,\lambda )$ -graph contains a Hamilton cycle for sufficiently large $n$ , assuming that $d\geq \log ^{6}n$ and $\lambda \leq cd$ , where $c=\frac {1}{70000}$ . This significantly improves a recent result of Glock, C…
View article: Regular bipartite decompositions of pseudorandom graphs
Regular bipartite decompositions of pseudorandom graphs Open
In 1972, Kotzig proved that for every even $n$, the complete graph $K_n$ can be decomposed into $\lceil\log_2n\rceil$ edge-disjoint regular bipartite spanning subgraphs, which is best possible. In this paper, we study regular bipartite dec…
View article: Hamiltonicity of Sparse Pseudorandom Graphs
Hamiltonicity of Sparse Pseudorandom Graphs Open
We show that every $(n,d,λ)$-graph contains a Hamilton cycle for sufficiently large $n$, assuming that $d\geq \log^{6}n$ and $λ\leq cd$, where $c=\frac{1}{70000}$. This significantly improves a recent result of Glock, Correia and Sudakov, …
View article: Dirac-type Problem of Rainbow matchings and Hamilton cycles in Random Graphs
Dirac-type Problem of Rainbow matchings and Hamilton cycles in Random Graphs Open
Given a family of graphs $G_1,\dots,G_{n}$ on the same vertex set $[n]$, a rainbow Hamilton cycle is a Hamilton cycle on $[n]$ such that each $G_c$ contributes exactly one edge. We prove that if $G_1,\dots,G_{n}$ are independent samples of…
View article: A stability result on matchings in 3-uniform hypergraphs
A stability result on matchings in 3-uniform hypergraphs Open
Let $n,s,k$ be three positive integers such that $1\leq s\leq(n-k+1)/k$ and let $[n]=\{1,\ldots,n\}$. Let $H$ be a $k$-graph with vertex set $\{1,\ldots,n\}$, and let $e(H)$ denote the number of edges of $H$. Let $ν(H)$ and $τ(H)$ denote t…