Xu Yang

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20242026

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4 papers · 1 filter

math.CO2026

Sharp Same-Color Cycle Covers in Two-Colored Complete Graphs

Xiao-Chuan Liu, Jonatas Teodomiro, Xu Yang

We extend the conjecture of Erdős and Gyárfás on monochromatic path covers to the setting of monochromatic cycle covers. We prove that, for all $n$ , every 2-edge-coloring of the co…

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 $χ'_…

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 Turán 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 Turán-type e…