Xiao-Chuan Liu

collaborators

4 papers

math.CO2026

Linear Lower Bounds for the Modular Chromatic Index

Xiao-Chuan Liu, Boyan Xu, Xu Yang

Let $k \geq 2$ be an integer. A $1 mod k$ edge-coloring of a graph $G$ is an edge-coloring in which every nonzero degree in each color class is congruent to $1$ modulo $k$ . Let $Ï'…

math.CO2026

Large Monochromatic Components in Colored Random Graphs

Xiao-Chuan Liu, Xu Yang

We study the size of the largest monochromatic connected component that must appear in any edge-coloring of a random graph. Let $G \sim G (n, p)$ with $p ≫ 1/ n$ and $p = o (1)$ , and wri…

math.CO2026

On TurÃ¡n Number of Graphs with Small Minimum Feedback Vertex Numbers

Xiao-Chuan Liu, Xu Yang

Given a graph $H$ , the minimum feedback vertex number of $H$ is the minimum number of vertices whose removal results in an acyclic graph. In this paper, we investigate TurÃ¡n-type…

math.CO2025

TurÃ¡n Number of Subdivisions of Multipartite Graphs

Xiao-Chuan Liu, Danni Peng, Xu Yang

In this paper, we investigate the TurÃ¡n exponent for $1$ -subdivisions of graphs that are neither bipartite nor complete. Specifically, we establish an upper bound on the TurÃ¡n nu…