Yangyang Cheng

Yangyang Cheng
University of Oxford | OX · Mathematical Institute

Dphil of Mathematics

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7
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Publications

Publications (7)
Preprint
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R\"{o}dl, Ruci\'{n}ski and Szemer\'{e}di proved that every $n$-vertex $k$-graph $H$, $k\geq3, \gamma>0$ and $n$ is sufficiently large, with $\delta_{k-1}(H)\geq(1/2+\gamma)n$ contains a tight Hamilton cycle, which can be seen as a generalization of Dirac's theorem in hypergraphs. In this paper, we extend this result to the rainbow setting as follow...
Preprint
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We study the following rainbow version of subgraph containment problems in a family of (hyper)graphs, which generalizes the classical subgraph containment problems in a single host graph. For a collection $\textbf{G}=\{G_1, G_2,\ldots, G_{m}\}$ of not necessarily distinct graphs on the same vertex set $[n]$, a (sub)graph $H$ on $[n]$ is rainbow if...
Preprint
For a set of positive integers $A \subseteq [n]$, an $r$-coloring of $A$ is rainbow sum-free if it contains no rainbow Schur triple. In this paper we initiate the study of the rainbow Erd\H{o}s-Rothchild problem in the context of sum-free sets, which asks for the subsets of $[n]$ with the maximum number of rainbow sum-free $r$-colorings. We show th...
Preprint
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Let $G_1,...,G_n$ be graphs on the same vertex set of size $n$, each graph having minimum degree $\delta(G_i)\geq \frac{n}{2}$. A recent conjecture of Aharoni asserts that there exists a rainbow Hamiltonian cycle i.e. a cycle with edge set $\{e_1,...,e_n\}$ such that $e_i\in E(G_i)$ for $1\leq i \leq n$. This can be seen as a rainbow variant of the...
Article
A subgraph H of an edge-colored graph G is called a properly colored subgraph if no two adjacent edges of H have the same color, and is called a rainbow subgraph if no two edges of H have the same color. For a vertex v of G, the color degree of v, denoted by dGc(v), is the number of distinct colors appeared in the edges incident with v. Let δc(G) b...
Article
The classical Dirac's theorem states that every graph G with order at least 3 and minimum degree δ(G)≥[Formula presented] contains a Hamiltonian cycle. Let G be an edge-colored graph. A subgraph of an edge-colored graph is called rainbow if all its edges have different colors. In 1980 Hahn conjectured that every properly edge-colored complete graph...
Article
The Ryser Conjecture which states that there is a transversal of size n in a Latin square of odd order n is equivalent to finding a rainbow matching of size n in a properly edge-colored Kn,n using n colors when n is odd. Let δ be the minimum degree of a graph. Wang proposed a more general question to find a function f(δ) such that every properly ed...

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