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 2014Show all

5 papers · 1 filter

math.CO2014

Planar graphs are 9/2-colorable

Daniel W. Cranston, Landon Rabern

We show that every planar graph $G$ has a 2-fold 9-coloring. In particular, this implies that $G$ has fractional chromatic number at most $\frac{9}{2}$ . This is the first proof (indepe…

math.CO2014

Yet another proof of Brooks' theorem

Landon Rabern

Arguably the simplest variation of this style of proof as we avoid reducing to the cubic case entirely.

math.CO2014

Improved lower bounds on the number of edges in list critical and online list critical graphs

Hal Kierstead, Landon Rabern

We prove that every $k$ -list-critical graph ( $k \geq 7$ ) on $n \geq k + 2$ vertices has at least $\frac{1}{2} (k - 1 + \frac{k - 3}{( k - c ) ( k - 1 ) + k - 3}) n$ edges where $c = (k-3)\left(…

math.CO2014

A note on coloring vertex-transitive graphs

Daniel W. Cranston, Landon Rabern

We prove bounds on the chromatic number $χ$ of a vertex-transitive graph in terms of its clique number $ω$ and maximum degree $Δ$ . We conjecture that every vertex-transitive graph…

math.CO2014★ 2 cited

Brooks' Theorem and Beyond

Daniel W. Cranston, Landon Rabern

We collect some of our favorite proofs of Brooks' Theorem, highlighting advantages and extensions of each. The proofs illustrate some of the major techniques in graph coloring, suc…