Zi-Xia Song

activity

20152026

most citedBreaking the degeneracy barrier for coloring graphs with no

K_{t}

minor

24 citations · 111 across the 46 of their papers we have counts for

collaborators

Showing 2022Show all

7 papers · 1 filter

math.CO2022

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, Bucić, Kalvari, Kuperwa…

math.CO2022

Every graph with no $K_{9}^{- 6}$ minor is $8$ -colorable

Michael Lafferty, Zi-Xia Song

For positive integers $t$ and $s$ , let $K_{t}^{- s}$ denote the family of graphs obtained from the complete graph $K_{t}$ by removing $s$ edges. A graph $G$ has no $\mathcal{K…

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.CO2022★ 22 cited

A Note on Odd Colorings of 1-Planar Graphs

Daniel W. Cranston, Michael Lafferty, Zi-Xia Song

A proper coloring of a graph is odd if every non-isolated vertex has some color that appears an odd number of times on its neighborhood. This notion was recently introduced by Petr…

math.CO2022

Planar Turán numbers of cubic graphs and disjoint union of cycles

Yongxin Lan, Yongtang Shi, Zi-Xia Song

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

Multicolor Ramsey Number for Double Stars

Every graph with no K9−6​ minor is 8-colorable

An improved lower bound for the planar Turán number of cycles

Every graph with no K8−4​ minor is 7-colorable

Properties of 8-contraction-critical graphs with no K7​ minor

A Note on Odd Colorings of 1-Planar Graphs

Planar Turán numbers of cubic graphs and disjoint union of cycles

Every graph with no $K_{9}^{- 6}$ minor is $8$ -colorable

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

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