Peter Bradshaw

activity

20242026

collaborators

12 papers

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

Density of rainbow triangles and properly colored $K_{4}$ 's

JÃ³zsef Balogh, Peter Bradshaw, Ramon I. Garcia +1

We establish a sharp upper bound on the number of properly $3$ -edge-colored $K_{4}$ 's in graphs with $R$ red, $G$ green and $B$ blue edges. We give a computer-free flag-algebra proof…

math.CO2026

A lower bound on the number of edges in DP-critical graphs

Peter Bradshaw, Ilkyoo Choi, Alexandr Kostochka +1

A graph $G$ is $k$ -critical (list $k$ -critical, DP $k$ -critical) if $I ¨ (G) = k$ ( $I ¨ _{ℓ} (G) = k$ , $I ¨ _{DP} (G) = k$ ) and for every proper subgraph $G^{'}$ of $G$ , $I ¨ (G^{'}) < k$ ($Ï_…

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 $I ¨ : E (G) \to N$ such that each color class forms an induced matching in $G$ . The strong chromatic inde…

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…

Density of list- and correspondence-critical graphs

DP vertex-arboricity of sparse graphs

Density of rainbow triangles and properly colored K4​'s

A lower bound on the number of edges in DP-critical graphs

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

Choosability of multipartite hypergraphs

Density of rainbow triangles and properly colored $K_{4}$ 's

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