Author

Peter Bradshaw

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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

Open access Jul 2026

Flexible List Coloring of Graphs With Maximum Average Degree Less Than 3

In the flexible list coloring problem, we consider a graph and a color list assignment on , as well as a subset for which each has a preferred color . Our goal is to find a proper ‐coloring of such that for at least vertices . We say that is ‐flexibly ‐choosable if for every ‐size list assignment on and every sub...

Richard Bi, Peter Bradshaw · Journal of Graph Theory · 0 citations