Tianyi Tao

collaborators

3 papers

math.CO2025

New lower bounds on the non-repetitive chromatic number of some graphs

Tianyi Tao, Junchi Zhang, Wentao Zhang +1

A graph $ G $ is said to be (vertex) non-repetitively colored if no simple path in $ G $ has a sequence of vertex colors that forms a repetition. Formally, a coloring \( c: V(G…

math.CO2025

On 1-11-representability and multi-1-11-representability of graphs

Mohammed Alshammari, Sergey Kitaev, Chaoliang Tang +2

Jeff Remmel introduced the concept of a $k$ -11-representable graph in 2017. This concept was first explored by Cheon et al. in 2019, who considered it as a natural extension of wor…

math.CO2024

The nonrepetitive colorings of grids

Tianyi Tao

For a graph $G$ , a vertex coloring $f$ is called nonrepetitive if for all $k \in N$ and all $P_{2 k} = ⟨ v_{1}, \dots, v_{k}, v_{k + 1}, \dots, v_{2 k} ⟩$ (path of $2 k$ ver…