D. Cranston

activity

20052026

most citedA Note on Odd Colorings of 1-Planar Graphs

22 citations · 92 across the 73 of their papers we have counts for

collaborators

Showing 2016Show all

3 papers · 1 filter

math.CO2016★ 1 cited

Short fans and the 5/6 bound for line graphs

Daniel W. Cranston, Landon Rabern

In 2011, the second author conjectured that every line graph $G$ satisfies $χ (G) \leq max {ω (G), \frac{5Δ ( G ) + 8}{6}}$ . This conjecture is best possible, as shown by replacing each ed…

math.CO2016

Planar Graphs have Independence Ratio at least 3/13

Daniel W. Cranston, Landon Rabern

The 4 Color Theorem (4CT) implies that every $n$ -vertex planar graph has an independent set of size at least $\frac{n}{4}$ ; this is best possible, as shown by the disjoint union of m…

math.CO2016

Edge Lower Bounds for List Critical Graphs, via Discharging

Daniel W. Cranston, Landon Rabern

A graph $G$ is $k$ -critical if $G$ is not $(k - 1)$ -colorable, but every proper subgraph of $G$ is $(k - 1)$ -colorable. A graph $G$ is $k$ -choosable if $G$ has an $L$ -coloring from eve…