4 citations · 20 across the 30 of their papers we have counts for
5 papers · 1 filter
Coloring graphs with dense neighborhoods
Landon Rabern
It is shown that any graph with maximum degree in which the average degree of the induced subgraph on the set of all neighbors of any vertex exceeds $\frac{6k^2}{6k^2 + 1}Δ+ k…
Coloring claw-free graphs with Δ-1 colors
Daniel W. Cranston, Landon Rabern
We prove that every claw-free graph that doesn't contain a clique on vertices can be colored.
A different short proof of Brooks' theorem
Landon Rabern
Lovász gave a short proof of Brooks' theorem by coloring greedily in a good order. We give a different short proof by reducing to the cubic case. Then we show how to extend the res…
A game generalizing Hall's theorem
Landon Rabern
We characterize the initial positions from which the first player has a winning strategy in a certain two-player game. This provides a generalization of Hall's theorem. Vizing's ed…
Partitioning and coloring with degree constraints
Landon Rabern
We prove that if is a vertex critical graph with for some and $ω(\fancy{H}(G)) \leq \frac{χ(G) + 1}{p + 1} - 2$, then $G = K_…