Peter Bradshaw

collaborators

2 papers

math.CO2024

A lower bound on the number of edges in DP-critical graphs. II. Four colors

Peter Bradshaw, Ilkyoo Choi, Alexandr Kostochka +1

A graph $G$ is $k$ -critical (list $k$ -critical, DP $k$ -critical) if $χ (G) = k$ ( $χ_{ℓ} (G) = k$ , $χ_{DP} (G) = k$ ) and for every proper subgraph $G^{'}$ of $G$ , $χ (G^{'}) < k$ ($χ_\ell(…

math.CO2024

Bipartite graphs are $(\frac{4}{5} - ε) \frac{Δ}{l o g Δ}$ -choosable

Peter Bradshaw, Bojan Mohar, Ladislav Stacho

Alon and Krivelevich conjectured that if $G$ is a bipartite graph of maximum degree $Δ$ , then the choosability (or list chromatic number) of $G$ satisfies $χ_{\ell}(G) = O \left (…

A lower bound on the number of edges in DP-critical graphs. II. Four colors

Bipartite graphs are (54​−ε)logΔΔ​-choosable

Bipartite graphs are $(\frac{4}{5} - ε) \frac{Δ}{l o g Δ}$ -choosable