Zi-Xia Song

collaborators

6 papers

math.CO2026

On the size of $(K_{t_{1}}, \dots, K_{t_{k}})$ -co-critical graphs

Zi-Xia Song

Given integers $k \geq 2$ and $t_{1}, \dots, t_{k} \geq 2$ , we write \emph{ $G \to (K_{t_{1}}, \dots, K_{t_{k}})$ } if every $k$ -coloring of the edges of a graph $G$ contains a monochrom…

math.CO2026

The ErdÅs-LovÃ¡sz Tihany Conjecture holds for all even-hole-free graphs

Zi-Xia Song

Let $s, t \geq 2$ be integers. A graph $G$ is $(s, t)$ -splittable if $V (G)$ can be partitioned into two sets $S$ and $T$ such that $I ¨ (G [S]) \geq s$ and $I ¨ (G [T]) \geq t$ . The ErdÅs-…

math.CO2026

Multicolor Ramsey Number for Double Stars

Jake Ruotolo, Zi-Xia Song

For a graph $H$ and an integer $k \geq 1$ , let $r (H; k)$ and $r_{ℓ} (H; k)$ denote the $k$ -color Ramsey number and list Ramsey number of $H$ , respectively. Alon, BuciÄ, Kalvari, Kuperw…

math.CO2025

Dominating Hadwiger's Conjecture for graphs $G$ with $I^\pm (G) = 2$

Michael Scully, Zi-Xia Song

Hadwiger's Conjecture from 1943 states that every graph with chromatic number $t$ contains a $K_{t}$ minor. Illingworth and Wood [arXiv:2405.14299] introduced the concept of a ``domi…

math.CO2025

Dominating Hadwiger's Conjecture holds for all $2 K_{2}$ -free graphs

Zi-Xia Song, Thomas Tibbetts

A dominating $K_{t}$ minor in a graph $G$ is a sequence $(T_{1}, \dots, T_{t})$ of pairwise disjoint non-empty connected subgraphs of $G$ , such that for $1 \leq i < j \leq t$ , every vertex in…

math.CO2025

Odd clique minors in graphs with independence number two

Yuqing Ji, Zi-Xia Song, Evan Weiss +1

A $K_{t}$ -expansion consists of $t$ vertex-disjoint trees, every two of which are joined by an edge. We call such an expansion odd if its vertices can be two-colored so that the edge…

On the size of (Kt1​​,…,Ktk​​)-co-critical graphs

The ErdÅs-LovÃ¡sz Tihany Conjecture holds for all even-hole-free graphs

Multicolor Ramsey Number for Double Stars

Dominating Hadwiger's Conjecture for graphs G with I^±(G)=2

Dominating Hadwiger's Conjecture holds for all 2K2​-free graphs

Odd clique minors in graphs with independence number two

On the size of $(K_{t_{1}}, \dots, K_{t_{k}})$ -co-critical graphs

The ErdÅs-LovÃ¡sz Tihany Conjecture holds for all even-hole-free graphs

Dominating Hadwiger's Conjecture for graphs $G$ with $I^\pm (G) = 2$

Dominating Hadwiger's Conjecture holds for all $2 K_{2}$ -free graphs