D. Cranston

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20152026

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math.CO2023

Equitable Coloring in 1-Planar Graphs

Daniel Cranston, Reem Mahmoud

For every $r \geq 13$ , we show every 1-planar graph $G$ with $Δ (G) \leq r$ has an equitable $r$ -coloring.

math.CO2023

Bounding Clique Size in Squares of Planar Graphs

Daniel W. Cranston

Wegner conjectured that if $G$ is a planar graph with maximum degree $Δ \geq 8$ , then $χ (G^{2}) \leq ⌊ \frac{3}{2} Δ ⌋ + 1$ . This problem has received much attention, but…