Landon Rabern

activity

20062008

most citedA Novel Proof of the Heine-Borel Theorem

1 citations · 2 across the 4 of their papers we have counts for

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math.CO2007

At Least Half Of All Graphs Satisfy χ\leq {1/4}ω+ {3/4}Δ+ 1

Landon Rabern

We prove that for any graph G at least one of G or $G ˉ$ satisfies $χ \leq 1/4 ω + 3/4 Δ + 1$ . In particular, self-complementary graphs satisfy this bound.

math.CO2006

New upper bounds on the chromatic number of a graph

landon rabern

We outline some ongoing work related to a conjecture of Reed \cite{reed97} on $ω$ , $Δ$ , and $χ$ . We conjecture that the complement of a counterexample $G$ to Reed's conjecture has…

math.CO2006★ 1 cited

A note on Reed's conjecture

landon rabern

In \cite{reed97}, Reed conjectures that the inequality $χ (G) \leq ⌈ 1/2 (ω (G) + Δ (G) + 1) ⌉$ holds for any graph $G$ . We prove this holds for a…

math.CO2006

Some bounds on convex combinations of $ω$ and $χ$ for decompositions into many parts

Landon Rabern

A \emph{ $k$ --decomposition} of the complete graph $K_{n}$ is a decomposition of $K_{n}$ into $k$ spanning subgraphs $G_{1}, ..., G_{k}$ . For a graph parameter $p$ , let $p (k; K_{n})$ denote the…

At Least Half Of All Graphs Satisfy χ\leq {1/4}ω+ {3/4}Δ+ 1

New upper bounds on the chromatic number of a graph

A note on Reed's conjecture

Some bounds on convex combinations of ω and χ for decompositions into many parts

Some bounds on convex combinations of $ω$ and $χ$ for decompositions into many parts