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 2013 · math.COShow all

2 papers · 2 filters

math.CO2013

Painting Squares in $Δ^{2} - 1$ Shades

Daniel W. Cranston, Landon Rabern

Cranston and Kim conjecture that if $G$ is a connected graph with maximum degree $Δ$ and $G$ is not a Moore Graph, then $χ_{l} (G^{2}) \leq Δ^{2} - 1$ ; here $χ_{l}$ is the list chromatic numbe…

math.CO2013

Graphs with $χ = Δ$ have big cliques

Daniel W. Cranston, Landon Rabern

Brooks' Theorem states that if a graph has $Δ \geq 3$ and $ω \leq Δ$ , then $χ \leq Δ$ . Borodin and Kostochka conjectured that if $Δ \geq 9$ and $ω \leq Δ - 1$ , then $χ \leq Δ - 1$ . We show that if…

Painting Squares in Δ2−1 Shades

Graphs with χ=Δ have big cliques

Painting Squares in $Δ^{2} - 1$ Shades

Graphs with $χ = Δ$ have big cliques