Author

Lin Tian

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Preprint Oct 2026

A note on the injective edge coloring of graphs with bounded maximum degree

Let $G$ be a graph. Under an \emph{injective edge coloring} of $G$, any two edges at distance $2$ or belonging to a common triangle receive distinct colors. The \emph{injective chromatic index} of $G$, denoted by $\chi'_{inj}(G)$, is the smallest integer $k$ such that $G$ admits an injective edge coloring with $k$ colo...

Lin Tian, Run-Ze Wang · 0 citations

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 Sep 2026

A stronger upper bound on the D-chromatic index

For a graph $G$, a proper edge coloring of $G$ is called a D-coloring if every diamond subgraph of $G$ is rainbow. Let $\chi'_D(G)$ be the D-chromatic index of $G$, which is the smallest integer $k$ such that $G$ admits a D-coloring with $k$ colors. Let $\Delta$ be the maximum degree of $G$. The only known Brooks-type...

Lin Tian, Run-Ze Wang · 0 citations