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 2016Show all

4 papers · 1 filter

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…

math.CO2016★ 1 cited

Hadwiger's conjecture for graphs with forbidden holes

Zi-Xia Song, Brian Thomas

Given a graph $G$ , the Hadwiger number of $G$ , denoted by $h (G)$ , is the largest integer $k$ such that $G$ contains the complete graph $K_{k}$ as a minor. A hole in $G$ is an induced…

math.CO2016★ 1 cited

Coloring Graphs with Forbidden Minors

Martin Rolek, Zi-Xia Song

Hadwiger's conjecture from 1943 states that for every integer $t \geq 1$ , every graph either can be $t$ -colored or has a subgraph that can be contracted to the complete graph on $t + 1$ …

math.CO2016★ 1 cited

Clique Minors in Double-critical Graphs

Martin Rolek, Zi-Xia Song

A connected $t$ -chromatic graph $G$ is \dfn{double-critical} if $G \ {u, v}$ is $(t - 2)$ -colorable for each edge $uv \in E (G)$ . A long standing conjecture of Erdős and Lová…