4 citations · 20 across the 30 of their papers we have counts for
6 papers · 2 filters
Extracting list colorings from large independent sets
Hal Kierstead, Landon Rabern
We take an application of the Kernel Lemma by Kostochka and Yancey to its logical conclusion. The consequence is a sort of magical way to draw conclusions about list coloring (and…
Beyond Degree Choosability
Daniel W. Cranston, Landon Rabern
Let be a connected graph with maximum degree . Brooks' theorem states that has a -coloring unless is a complete graph or an odd cycle. A graph is \emph{degree…
List-coloring claw-free graphs with -1 colors
Daniel W. Cranston, Landon Rabern
We prove that if is a quasi-line graph with and , then . Together with our previous work, this implies that if is a claw-free g…
Edge-coloring via fixable subgraphs
Daniel W. Cranston, Landon Rabern
Many graph coloring proofs proceed by showing that a minimal counterexample to the theorem being proved cannot contain certain configurations, and then showing that each graph unde…
Subcubic edge chromatic critical graphs have many edges
Daniel W. Cranston, Landon Rabern
We consider graphs with such that and for every edge , so-called \emph{critical} graphs. Jakobsen noted that the Petersen graph with a vertex del…
The Fractional Chromatic Number of the Plane
Daniel W. Cranston, Landon Rabern
The chromatic number of the plane is the chromatic number of the uncountably infinite graph that has as its vertices the points of the plane and has an edge between two points if t…