Zi‐Xia Song

activity

20162024

most citedAn improved lower bound for the planar Turán number of cycles

2 citations · 3 across the 7 of their papers we have counts for

collaborators

7 papers

math.CO2024

On tight $(k, ℓ)$ -stable graphs

Xiaonan Liu, Zi-Xia Song, Zhiyu Wang

For integers $k > ℓ \geq 0$ , a graph $G$ is $(k, ℓ)$ -stable if $α (G - S) \geq α (G) - ℓ$ for every $S \subseteq V (G)$ with $∣ S ∣ = k$ . A recent result of Dong and Wu [SIAM J. Discrete Mat…

math.CO2023

Minimizing the number of edges in $(C_{4}, K_{1, k})$ -co-critical graphs

Gang Chen, Chenchen Ren, Zi-Xia Song

Given graphs $H_{1}, H_{2}$ , a {red, blue}-coloring of the edges of a graph $G$ is a critical coloring if $G$ has neither a red $H_{1}$ nor a blue $H_{2}$ . A non-complete graph $G$ is $(H…

math.CO2022★ 2 cited

An improved lower bound for the planar Turán number of cycles

Yongxin Lan, Zi-Xia Song

The planar Turán number of a graph $H$ , denoted by $e x_{_{P}} (n, H)$ , is the largest number of edges in a planar graph on $n$ vertices without containing $H$ as a subgraph.…

math.CO2022

Every graph with no $K_{8}^{- 4}$ minor is $7$ -colorable

Michael Lafferty, Zi-Xia Song

Hadwiger's Conjecture from 1943 states that every graph with no $K_{t}$ minor is $(t - 1)$ -colorable; it remains wide open for all $t \geq 7$ . For positive integers $t$ and $s$ , let $\…

math.CO2022

Properties of $8$ -contraction-critical graphs with no $K_{7}$ minor

Martin Rolek, Zi-Xia Song, Robin Thomas

Motivated by the famous Hadwiger's Conjecture, we study the properties of $8$ -contraction-critical graphs with no $K_{7}$ minor; we prove that every $8$ -contraction-critical graph wi…

math.CO2016

Double-critical graph conjecture for claw-free graphs

Martin Rolek, Zi-Xia Song

A connected graph $G$ with chromatic number $t$ is double-critical if $G \ {x, y}$ is $(t - 2)$ -colorable for each edge $x y \in E (G)$ . The complete graphs are the only k…

On tight (k,ℓ)-stable graphs

Minimizing the number of edges in (C4​,K1,k​)-co-critical graphs