Zhifei Yan

activity

20242026

collaborators

12 papers

math.CO2026

A rainbow version of Lehel's conjecture

Pedro Araújo, Xiao-Chuan Liu, Taísa Martins +4

Lehel's conjecture states that every 2-edge-colouring of K_n admits a partition of its vertex set into two monochromatic cycles. It was proven for sufficiently large n by Łuczak, R…

math.CO2026

Tight Staircase Bounds for Cyclic Subsets below Dirac's Threshold

Hong Liu, Mengyuan Niu, Lanchao Wang +1

Let $Cyc (G)$ denote the number of cyclic subsets in a graph $G$ , which are subsets that induce a Hamiltonian subgraph. Draganić, Keevash and Müyesser recently proved…

math.CO2026

The sharp threshold for rainbow stackings of random edge-colourings

Hong Liu, Guorui Ma, Yangrui Xiang +1

A rainbow stacking of $m$ independent, uniformly random $r$ -edge-colourings of $K_{n}$ is a tuple of vertex permutations that superimposes the colourings such that no two edges of th…

math.CO2026

Constructor--Blocker games forbidding even cycles

Lanchao Wang, Zhifei Yan

The Constructor--Blocker game is played on the edge set of $K_{n}$ . Two players alternately claim previously unclaimed edges. Constructor aims to maximize the number of copies of a t…

math.CO2026

Structural Reductions for Monochromatic Matchings and Ramsey Tilings

Hong Liu, Maksim Turevskii, Lanchao Wang +1

The Alon--Frankl--Lovász theorem determines the chromatic number of Kneser hypergraphs; equivalently, it gives the sharp minimum size of a monochromatic matching in every edge-colo…

math.CO2026

Sharp threshold for Hamilton cycles in randomly perturbed sparse graphs

Guorui Ma, Zhifei Yan

We determine the sharp threshold for Hamilton cycles in randomly perturbed sparse graphs. For any $α = α (n) = o (1)$ , let $G_{α}$ be an $n$ -vertex graph with minimum degree $δ (G_{α}) \geq α n$ .…

math.CO2026

Ramsey properties for tilings in random graphs

Lucas Aragão, Xinbu Cheng, Rafael Filipe +3

Let $m H$ be the graph formed by $m$ vertex-disjoint copies of a graph $H$ . Let $G \to (H)_{r}$ denote that, in any $r$ -colouring of the edges of $G$ , there exists a monochromatic cop…

math.CO2026

Triangle packings in randomly perturbed graphs

Xinbu Cheng, Hong Liu, Lanchao Wang +1

The longstanding Nash-Williams conjecture asserts that every $K_{3}$ -divisible graph $G$ with $δ (G) \geq 3 n /4$ admits a triangle decomposition. In the random setting, Frankl and Rödl s…

math.CO2026

Colour diversity in spanning structures under Dirac-type conditions

Xinbu Cheng, Xinqi Huang, Hong Liu +2

Finding spanning structures with many distinct colours in properly edge-coloured graphs is a central theme in extremal combinatorics. A classical result of Andersen shows that ever…

math.CO2025

Colour-biased Hamilton cycles in randomly perturbed graphs

Wenchong Chen, Xinbu Cheng, Zhifei Yan

Given a graph $G$ and an $r$ -edge-colouring $χ$ on $E (G)$ , a Hamilton cycle $H \subset G$ is said to have $t$ colour-bias if $H$ contains $n / r + t$ edges of the same colour in $χ$ . Fr…

math.CO2024

Near rainbow Hamilton cycles in dense graphs

Danni Peng, Zhifei Yan

Finding near-rainbow Hamilton cycles in properly edge-coloured graphs was first studied by Andersen, who proved in 1989 that every proper edge colouring of the complete graph on $n…

math.CO2024

The chromatic number of very dense random graphs

Zhifei Yan

The chromatic number of a very dense random graph $G (n, p)$ , with $p \geq 1 - n^{- c}$ for some constant $c > 0$ , was first studied by Surya and Warnke, who conjectured that the typic…