Luke Postle

activity

20162025

most citedConnectivity and choosability of graphs with no

K_{t}

minor

8 citations · 11 across the 9 of their papers we have counts for

collaborators

Showing 2021Show all

3 papers · 1 filter

math.CO2021

Five-List-Coloring Graphs on Surfaces: The Many Faces Far-Apart Generalization of Thomassen's Theorem

Luke Postle, Robin Thomas

Let $G$ be a plane graph with $C$ the boundary of the outer face and let $(L (v) : v \in V (G))$ be a family of non-empty sets. By an $L$ -coloring of a subgraph $J$ of $G$ we mean a (pr…

math.CO2021

Triangle-free planar graphs with at most $6 4^{n^{0.731}}$ 3-colorings

Zdeněk Dvořák, Luke Postle

Thomassen conjectured that triangle-free planar graphs have exponentially many 3-colorings. Recently, he disproved his conjecture by providing examples of such graphs with $n$ vert…

math.CO2021

Structure in sparse $k$ -critical graphs

Ron Gould, Victor Larsen, Luke Postle

Recently, Kostochka and Yancey proved that a conjecture of Ore is asymptotically true by showing that every $k$ -critical graph satisfies $|E(G)|\geq\left\lceil\left(\frac{k}{2}-\fr…

Five-List-Coloring Graphs on Surfaces: The Many Faces Far-Apart Generalization of Thomassen's Theorem

Triangle-free planar graphs with at most 64n0.731 3-colorings

Structure in sparse k-critical graphs

Triangle-free planar graphs with at most $6 4^{n^{0.731}}$ 3-colorings

Structure in sparse $k$ -critical graphs