D. Cranston

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20152021

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4 papers · 1 filter

math.CO2021

Star coloring of sparse graphs

Yuehua Bu, Daniel W. Cranston, Mickaël Montassier +2

A proper coloring of the vertices of a graph is called a \emph{star coloring} if the union of every two color classes induces a star forest. The star chromatic number $χ_{s} (G)$ is t…

math.CO2018

Circular Flows in Planar Graphs

Daniel W. Cranston, Jiaao Li

For integers $a \geq 2 b > 0$ , a \emph{circular $a / b$ -flow} is a flow that takes values from ${\pm b, \pm (b + 1), \dots, \pm (a - b)}$ . The Planar Circular Flow Conjecture states that ever…

math.CO2018

A Note on Bootstrap Percolation Thresholds in Plane Tilings using Regular Polygons

Neal Bushaw, Daniel W. Cranston

In \emph{ $k$ -bootstrap percolation}, we fix $p \in (0, 1)$ , an integer $k$ , and a plane graph $G$ . Initially, we infect each face of $G$ independently with probability $p$ . Infected…

math.CO2015

List-coloring the Square of a Subcubic Graph

Daniel W. Cranston, Seog-Jin Kim

The {\em square} $G^{2}$ of a graph $G$ is the graph with the same vertex set as $G$ and with two vertices adjacent if their distance in $G$ is at most 2. Thomassen showed that every…