1 citations · 2 across the 4 of their papers we have counts for
5 papers
A Novel Proof of the Heine-Borel Theorem
Matthew Macauley, Brian Rabern, Landon Rabern
Every beginning real analysis student learns the classic Heine-Borel theorem, that the interval [0,1] is compact. In this article, we present a proof of this result that doesn't in…
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 satisfies . In particular, self-complementary graphs satisfy this bound.
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 , , and . We conjecture that the complement of a counterexample to Reed's conjecture has…
A note on Reed's conjecture
landon rabern
In \cite{reed97}, Reed conjectures that the inequality holds for any graph . We prove this holds for a…
Some bounds on convex combinations of and for decompositions into many parts
Landon Rabern
A \emph{--decomposition} of the complete graph is a decomposition of into spanning subgraphs . For a graph parameter , let denote the…