Author

Zimu Xiang

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Preprint Aug 2026

List coloring $C_3$-free planar graphs with a sparse matching of restricted lists

A graph $G$ is $k$-choosable if it has a proper coloring for every $k$-list assignment. While every $C_3$-free planar graph is $4$-choosable, some of them are not $3$-choosable, as constructed by Voigt. Hu and Zhu conjectured that if $G$ is a $C_3$-free planar graph and $X \subseteq V(G)$ induces a bipartite subgraph,...

S. Hartke, Yu-Pei Li, Joseph Pappe et al. · 0 citations

Preprint Jul 2026

DP vertex-arboricity of sparse graphs

The vertex arboricity $\mathrm{va}(G)$ of a multigraph $G$ is the minimum number $k$ for which $V(G)$ can be partitioned into $k$ subsets, each of which induces an acyclic subgraph of $G$. By definition, if $\mathrm{va}(G)= k$, then the chromatic number, $\chi(G)$, satisfies $k\leq \chi(G)\leq 2k$. Fundamental results...

Peter Bradshaw, Alexandr V. Kostochka, Zimu Xiang · 0 citations