Xinbu Cheng

activity

20242026

collaborators

6 papers

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 $I^´ (G) \geq 3 n /4$ admits a triangle decomposition. In the random setting, Frankl and RÃ¶dl…

math.CO2026

On the TurÃ¡n number of blow-ups of $F_{5}$

Xiamiao Zhao, Xin Cheng, DÃ¡niel Gerbner +4

Let $F_{5}$ denote the $3$ -uniform hypergraph on the vertex set ${f_{1}, f_{2}, \dots, f_{5}}$ with hyperedges ${f_{1} f_{2} f_{3}, f_{1} f_{2} f_{4}, f_{3} f_{4} f_{5}}$ . Recently, Balogh, Clemen and Lu…

math.CO2026

Ramsey properties for tilings in random graphs

Lucas AragÃ£o, 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

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 $I ¨ $ 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 $I ¨ $ .…

math.CO2024

Sublinear hitting sets for some geometric graphs

Xinbu Cheng, Xinqi Huang, Mingyuan Rong +1

For an $n$ -vertex graph $G$ , let $h (G)$ denote the smallest size of a subset of $V (G)$ such that it intersects every maximum independent set of $G$ . A conjecture posed by BollobÃ¡s…

Triangle packings in randomly perturbed graphs

On the TurÃ¡n number of blow-ups of F5​

Ramsey properties for tilings in random graphs

Colour diversity in spanning structures under Dirac-type conditions

Colour-biased Hamilton cycles in randomly perturbed graphs

Sublinear hitting sets for some geometric graphs

On the TurÃ¡n number of blow-ups of $F_{5}$