Author

Abhishek Dhawan

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Preprint Sep 2026

Fractional DP-colorings of $d$-degenerate locally sparse graphs

Bernshteyn, Kostochka, and Zhu (2020) introduced the notion of fractional DP-coloring, which generalizes both fractional coloring and fractional list coloring. Among several foundational results, they proved that every $d$-degenerate bipartite graph $G$ satisfies $\chi_f^{\mathrm{DP}} \le (1 + o(1))\frac{d}{\log d}$, a...

Abhishek Dhawan, Huy Nguyen, R. Rathi · 0 citations

Jul 2026

Sharp bounds for the fractional chromatic number of high-girth d-degenerate graphs

Martinsson and Steiner recently proved that the fractional chromatic number of any $d$-degenerate triangle-free graph $G$ satisfies $\chi_f(G) = O\left(\frac{d}{\log d}\right)$. They further conjectured a sharp leading constant $1 + o(1)$. In this paper, we confirm their upper bound conjecture for graphs having girth a...

Peter Allen, Abhishek Dhawan, Jonathan A. Noel · arXiv.org · 3 citations