Peter Bradshaw

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20242026

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12 papers · 1 filter

math.CO2026

Density of list- and correspondence-critical graphs

Peter Bradshaw

A graph $G$ is list $k$ -critical if $G$ is not $(k - 1)$ -list-colorable, but every proper subgraph of $G$ is $(k - 1)$ -list-colorable. In this paper, we study the function $f_{\ell}(n,…

math.CO2026

DP vertex-arboricity of sparse graphs

Peter Bradshaw, Alexandr Kostochka, Zimu Xiang

The vertex arboricity $va (G)$ 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…

math.CO2026

The strong chromatic index of $K_{t, t}$ -free graphs

Richard Bi, Peter Bradshaw, Abhishek Dhawan +1

A strong edge coloring of a graph $G$ is an edge coloring $ϕ : E (G) \to N$ such that each color class forms an induced matching in $G$ . The strong chromatic index…

math.CO2025

Choosability of multipartite hypergraphs

Peter Bradshaw, Abhishek Dhawan, Nhi Dinh +2

A $k$ -uniform hypergraph (or $k$ -graph) $H = (V, E)$ is $k$ -partite if $V$ can be partitioned into $k$ sets $V_{1}, \dots, V_{k}$ such that each edge in $E$ contains precisely one ver…

math.CO2025

Flexible DP 3-coloring of sparse multigraphs

Peter Bradshaw, Ilkyoo Choi, Alexandr Kostochka

A \emph{request} on a graph assigns a preferred color to a subset of the vertices. A graph $G$ is \emph{ $ε$ -flexibly $k$ -choosable} if for every $k$ -list assignment $L$ and every r…

math.CO2025

Toward Vu's conjecture

Peter Bradshaw, Abhishek Dhawan, Abhishek Methuku +1

In 2002, Vu conjectured that graphs of maximum degree $Δ$ and maximum codegree at most $ζ Δ$ have chromatic number at most $(ζ + o (1)) Δ$ . Despite its importance, the conjecture has re…

Density of list- and correspondence-critical graphs

DP vertex-arboricity of sparse graphs

The strong chromatic index of Kt,t​-free graphs

Choosability of multipartite hypergraphs

Flexible DP 3-coloring of sparse multigraphs

Toward Vu's conjecture

The strong chromatic index of $K_{t, t}$ -free graphs