4 citations · 20 across the 30 of their papers we have counts for
38 papers
Structural fixed-point theorems
Brian Rabern, Landon Rabern
The semantic paradoxes are associated with self-reference or referential circularity. However, there are infinitary versions of the paradoxes, such as Yablo's paradox, that do not…
Playing cards with Vizing's demon
Brian Rabern, Landon Rabern
We analyze a solitaire game in which a demon rearranges some cards after each move. The graph edge coloring theorems of Kőnig (1931) and Vizing (1964) follow from the winning strat…
Coloring -free graphs with colors
Daniel W. Cranston, Hudson Lafayette, Landon Rabern
The Borodin-Kostochka Conjecture states that for a graph , if and , then . We prove the Borodin-Kostochka Conjecture for $(P_5,…
The Hilton--Zhao Conjecture is True for Graphs with Maximum Degree 4
Daniel W. Cranston, Landon Rabern
A simple graph is \emph{overfull} if . By the pigeonhole principle, every overfull graph has . The \emph{core} of a graph, denoted…
Short fans and the 5/6 bound for line graphs
Daniel W. Cranston, Landon Rabern
In 2011, the second author conjectured that every line graph satisfies . This conjecture is best possible, as shown by replacing each ed…
Planar Graphs have Independence Ratio at least 3/13
Daniel W. Cranston, Landon Rabern
The 4 Color Theorem (4CT) implies that every -vertex planar graph has an independent set of size at least ; this is best possible, as shown by the disjoint union of m…