Landon Rabern

1 citations · 3 across the 4 of their papers we have counts for

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math.CO2011★ 1 cited

A note on vertex partitions

Landon Rabern

We prove a general lemma about partitioning the vertex set of a graph into subgraphs of bounded degree. This lemma extends a sequence of results of Lovász, Catlin, Kostochka and Ra…

math.CO2011★ 1 cited

Destroying Non-Complete Regular Components in Graph Partitions

Landon Rabern

We prove that if $G$ is a graph and $r_{1}, ..., r_{k} \in Z_{\geq 0}$ such that $\sum_{i = 1}^{k} r_{i} \geq Δ (G) + 2 - k$ then $V (G)$ can be partitioned into sets $V_{1}, ..., V_{k}$ …

math.CO2011

Coloring $Δ$ -Critical Graphs With Small High Vertex Cliques

Landon Rabern

We prove that $K_{χ (G)}$ is the only critical graph $G$ with $χ (G) \geq Δ (G) \geq 6$ and $ω (H (G)) \leq ⌊ \frac{Δ ( G )}{2} ⌋ - 2$ . Here $\mathcal{H}…

math.CO2011★ 1 cited

An improvement on Brooks' Theorem

Landon Rabern

We prove that $χ (G) \leq max ω (G), Δ_{2} (G), (5/6) (Δ (G) + 1)$ for every graph $G$ with $Δ (G) \geq 3$ . Here $Δ_{2}$ is the parameter introduced by Stacho that gives the largest degre…

A note on vertex partitions

Destroying Non-Complete Regular Components in Graph Partitions

Coloring Δ-Critical Graphs With Small High Vertex Cliques

An improvement on Brooks' Theorem

Coloring $Δ$ -Critical Graphs With Small High Vertex Cliques