Author

Zhi-Jun Lu

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Preprint Sep 2026

$(2,\mathcal{F})$-Avoiding Coloring and B-Coloring under Bipartite Exclusions

Let $\mathcal{F}$ be a nonempty family of connected bipartite graphs, each with at least two edges. For a graph $G$, a proper vertex coloring of $G$ is $(2,\mathcal{F})$-avoiding if no member of $\mathcal{F}$ occurs bichromatically, and $\chi_{2,\mathcal{F}}(G)$ denotes the minimum number of colors in such a coloring....

Zhi-Jun Lu, Qi-Rui Ying, Hui-Min Song · 0 citations

Preprint Aug 2026

Proper Conflict-Free Choosability for Graphs with Bounded Average Degree

For a graph $G$, a proper coloring of $G$ is called proper conflict-free if for every non-isolated vertex $u$, there is at least one color appearing exactly once in $N_G(u)$. A graph $G$ is proper conflict-free $f$-choosable if for every list assignment $L$ with $|L(v)|\ge f(v)$ for each vertex $v$, $G$ admits a proper...

Zhi-Jun Lu, Qi-Rui Ying, Hui-Min Song · 1 citation