Landon Rabern

activity

20062021

most citedPartitioning and coloring with degree constraints

4 citations · 20 across the 30 of their papers we have counts for

collaborators

Showing 2016 · math.COShow all

5 papers · 2 filters

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

A better lower bound on average degree of k-list-critical graphs

Landon Rabern

We improve the best known bounds on average degree of $k$ -list-critical graphs for $k \geq 6$ . Specifically, for $k \geq 7$ we show that every non-complete $k$ -list-critical graph ha…

math.CO2016

A better lower bound on average degree of 4-list-critical graphs

Landon Rabern

This short note proves that every incomplete $k$ -list-critical graph has average degree at least $k - 1 + \frac{k - 3}{k ^{2} - 2 k + 2}$ . This improves the best known bound for $k = 4, 5, 6$ . T…

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…