Peter Bradshaw

activity

20232026

collaborators

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4 papers · 1 filter

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

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

József 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.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…

Choosability of multipartite hypergraphs

Density of rainbow triangles and properly colored K4​'s

Flexible DP 3-coloring of sparse multigraphs

Toward Vu's conjecture

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